GWB Reaction Modeling Guide

The Geochemist’s Workbench®

Release 12

GWB

Reaction Modeling Guide

The Geochemist’s Workbench® Release 12

GWB Reaction

Modeling Guide

Craig M. Bethke Brian Farrell

Sharon Yeakel

Aqueous Solutions, LLC Champaign, Illinois

Printed August 31, 2021

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Cover photo: Salinas de Janubio by Jorg Hackemann

v

Contents

Chapter List Contents .................................................................................................... v Detailed Contents .................................................................................... vii Introduction .............................................................................................. 1 Getting Started with React ........................................................................ 5 Tracing Reaction Paths............................................................................ 19 Kinetic Reaction Paths ............................................................................ 59 Custom Rate Laws ................................................................................. 115 Using Gtplot ........................................................................................... 133 Using Phase2 ......................................................................................... 143 Using P2plot .......................................................................................... 179 Appendix: Further Reading .................................................................... 195

vi

vii

Detailed Contents

Contents .................................................................................................... v Detailed Contents .................................................................................... vii Introduction .............................................................................................. 1

1.1 React program ......................................................................................................... 1 1.2 Gtplot program ........................................................................................................ 2 1.3 Phase2 program ...................................................................................................... 2 1.4 P2plot program ....................................................................................................... 2 1.5 Example input files .................................................................................................. 3

Getting Started with React ........................................................................ 5

2.1 Conceptual model ................................................................................................... 5 2.2 Example calculation ................................................................................................ 6 2.3 Initial system ........................................................................................................... 9 2.4 Redox disequilibrium ............................................................................................ 12 2.5 Activity coefficients ............................................................................................... 12 2.6 Sorption onto mineral surfaces ............................................................................ 13 2.7 Settable variables.................................................................................................. 13 2.8 Controlling the printout ........................................................................................ 16 2.9 React command line ............................................................................................. 18

Tracing Reaction Paths............................................................................ 19

3.1 Titration paths ....................................................................................................... 19 3.2 Flow-through model ............................................................................................. 26 3.3 Flush model ........................................................................................................... 30 3.4 Polythermal reaction paths .................................................................................. 32 3.5 Buffered paths ....................................................................................................... 35 3.6 Sliding activity and fugacity .................................................................................. 38 3.7 “Flash diagrams” ................................................................................................... 45 3.8 Fractionation of stable isotopes ........................................................................... 49 3.9 Picking up the results of a run .............................................................................. 56

Kinetic Reaction Paths ............................................................................ 59

4.1 Setting kinetic reactions ....................................................................................... 59

viii

4.2 Kinetics of precipitation and dissolution .............................................................. 63

4.2.1 Promoting and inhibiting species .............................................................................. 67 4.2.2 Nonlinear rate laws ..................................................................................................... 70 4.2.3 Cross-affinity rate laws ............................................................................................... 71 4.2.4 Nucleation ................................................................................................................... 72

4.3 Forward and reverse reactions ............................................................................. 74 4.4 Kinetics of complexation and sorption ................................................................. 76 4.5 Gas transfer kinetics .............................................................................................. 83 4.6 Kinetics of redox reactions .................................................................................... 86

4.6.1 Catalysis on mineral surfaces ..................................................................................... 92 4.6.2 Enzymes and biotransformations .............................................................................. 96

4.7 Microbial metabolism and growth ...................................................................... 102

4.7.1 Metabolic rate ........................................................................................................... 103 4.7.2 Relationship to other rate laws ................................................................................ 106 4.7.3 Example calculation ................................................................................................. 107

4.8 Chaining together kinetic paths .......................................................................... 112

Custom Rate Laws .................................................................................. 115

5.1 Setting the rate law form directly ....................................................................... 115 5.2 Rate law scripts .................................................................................................... 116 5.3 Compiled rate laws .............................................................................................. 120

Using Gtplot ........................................................................................... 133

6.1 Initial plot ............................................................................................................. 133 6.2 XY Plot configuration ........................................................................................... 135 6.3 Plot types ............................................................................................................. 137 6.4 Editing plot appearance ...................................................................................... 137 6.5 Scatter data .......................................................................................................... 137 6.6 Loading and saving plot configuration ............................................................... 138 6.7 Exporting the plot ................................................................................................ 138 6.8 Gtplot command line ........................................................................................... 141

Using Phase2 .......................................................................................... 143

7.1 Conceptual model ............................................................................................... 143 7.2 Staging and scanning paths ................................................................................ 144 7.3 Progress variables................................................................................................ 148 7.4 Linear and log stepping ....................................................................................... 149 7.5 Settable variables ................................................................................................ 150 7.6 Multicore execution ............................................................................................. 152

ix

7.7 Running a model ................................................................................................. 152 7.8 Example: Speciation diagram ............................................................................. 154 7.9 Example: Mineral solubility ................................................................................. 158 7.10 Example: Oxygen solubility ............................................................................... 161 7.11 Example: Isotope fractionation ........................................................................ 164 7.12 Example: Surface complexation ....................................................................... 167 7.13 Example: Kinetic diagram ................................................................................. 171 7.14 Cross-section plots ............................................................................................ 175 7.15 Phase2 command line ....................................................................................... 178

Using P2plot .......................................................................................... 179

8.1 2D Diagram .......................................................................................................... 180

8.1.1 Predominance Maps .................................................................................................. 182 8.1.2 Assemblage Maps ...................................................................................................... 186 8.1.3 Axis Variables ............................................................................................................. 188

8.2 Cross-section Plot configuration ........................................................................ 188 8.3 Plot types ............................................................................................................. 191 8.4 Editing plot appearance...................................................................................... 191 8.5 Scatter data ......................................................................................................... 191 8.6 Loading and saving plot configuration .............................................................. 192 8.7 Exporting the plot ............................................................................................... 192 8.8 P2plot command line .......................................................................................... 193

Appendix: Further Reading .................................................................... 195

A.1 Reaction modeling .............................................................................................. 195 A.2 Geochemical kinetics .......................................................................................... 196 A.3 Isotopic modeling ............................................................................................... 196 A.4 Compilers and interpreters ................................................................................ 196

1

Introduction

In geochemical reaction modeling, as the name suggests, you construct numerical simulations of reactions that might occur in the geochemical environment. You might, for example, wish to model the consequences of a specific fluid reacting with a certain set of minerals. For a detailed description of such modeling, as well as a large number of fully worked examples, please see the Geochemical and Biogeochemical Reaction Modeling text by Craig M. Bethke, available from Cambridge University Press and booksellers such as Amazon.

In The Geochemist’s Workbench, you use React to trace reaction models and Gtplot to render graphically the results of React simulations.

1.1 React program React is a flexible program that models equilibrium states and geochemical processes in systems that contain an aqueous fluid. Like SpecE8, React can calculate the equilibrium distribution of aqueous species in a fluid, a fluid’s saturation state with respect to minerals, and the fugacity and partial pressure of gases dissolved in a fluid.

The program can also trace the evolution of a system as it undergoes reversible or irreversible reaction in an open or closed system, either at a given temperature or polythermally. React can integrate kinetic rate laws and simulate the fractionation of stable isotopes in a reacting system.

React is, in fact, an extension of program SpecE8, which is described in the GWB Essentials Guide, in the section Using SpecE8. You should, therefore, become familiar with SpecE8 and its documentation before beginning to work with React.

The next three sections of this manual introduce the program, show how to construct reaction paths, show how to trace kinetic reaction paths, and give details on constructing custom rate laws.

2 GWB Reaction Modeling

1.2 Gtplot program Gtplot is used to render the results of React simulations graphically. The program is driven interactively, using the mouse, and offers the capability of displaying reaction models in a variety of ways. The Using Gtplot section of this manual shows how to use this program.

1.3 Phase2 program Phase2 is a program for calculating phase and predominance diagrams of virtually any type. The program works by tracing a series of stacked reaction paths across the diagram. Each traverse is conceptually identical to a React simulation. As such, Phase2 can account not only for multicomponent chemical equilibrium, but reaction kinetics, external buffers, sorption and surface complexation, stable isotope fractionation, and, in fact, any of React’s many capabilities.

A Phase2 diagram differs from a simple diagram of the type constructed by Act2 and Tact in that each point in the diagram represents the complete solution to the equations describing the system’s distribution of mass. If you were to use Phase2 to calculate an Eh-pH diagram, for example, you would find that, unlike the result from Act2, the boundary lines are curved, rather than linear. Because of the calculation’s completeness, some Phase2 diagrams differ qualitatively from their Act2 counterparts. For this reason, the diagrams are sometimes referred to as “true” Eh-pH or “true” activity diagrams.

Phase2 diagrams, furthermore, can be plotted over a wide range of variable choices, and in a variety of ways. To learn more about Phase2 and its abilities, visit the Using Phase2 section of this manual.

1.4 P2plot program P2plot is used to render the results of Phase2 simulations graphically. The program is similar to Gtplot and Xtplot, which are described in the Using Gtplot section of this manual and the Using Xtplot section of GWB Reactive Transport Modeling Guide, respectively. Specifically, P2plot can diagram phase assemblages, predominant phases and species, gas pressures, isotope compositions, and even cross sections through the diagram. The Using P2plot section of this manual shows how to use this program.

Introduction 3

1.5 Example input files Subsequent chapters of this manual contain examples of applying React to trace reaction models in various configurations, and using Phase2 to create diagrams of differing types. An input file corresponding to each example is available in the GWB installation directory (e.g., “\Program Files\GWB”) under the subdirectory “Script”.

The example files for program React are: “Feldspar.rea” Reaction with potassium feldspar “Dolomite.rea” Pumping waste into an injection well “IonEx.rea” Titration path with an Ion exchange reaction “Evaporate.rea” Evaporation of seawater “Flush.rea” Reactive fluid migration through quartzite “Steam.rea” Steam flood passing through a reservoir “Pyrite.rea” Dissolution of pyrite “Degas.rea” Gas escaping from a groundwater “Uranium.rea” Distribution of Uranium species “Surface.rea” Surface complexation “Flash.rea” Mixing of two fluids “Isotope.rea” Tracing stable isotope fractionation “Kinetic.rea” Tracing the kinetic dissolution of Albite “Albite.rea” Kinetic dissolution with promoting species “Nonlinear.rea” Nonlinear rate laws “Assosciation.rea” Kinetics of complexation “Desorption.rea” Kinetics of sorption “GasTransfer.rea” Kinetics of degassing “Redox.rea” Kinetics of redox reactions “Catalysis.rea” Catalysis on minerals surfaces “Enzyme.rea” Enzymes and biotransformations “Microbes.rea” Microbial metabolism and growth

The example Phase2 files are: “CuSH2O.ph2” Speciation diagram “AlSolubility.ph2” Mineral solubility “O2Solubility.ph2” Oxygen solubility “CO2_frac.ph2” Isotope fractionation “ZnSorption.ph2” Surface complexation “Promoting.ph2” Kinetic diagram


5

Getting Started with React

React, as described in the Introduction to this guide, is a program designed for modeling irreversible reaction process in geochemical systems. This section provides an introduction to the program, and subsequent sections give details on constructing various types of reaction paths, accounting for kinetic reactions, and constructing custom rate laws.

2.1 Conceptual model A React model calculation has two main components: the initial system and the process that alters it.

React begins a simulation by calculating the system’s initial equilibrium state. The program then changes the system by adding (or removing) reactants to vary the system’s composition, changing the temperature, or varying the fugacity of gases in an external buffer. This process is the reaction path; a representation is shown below.


In the figure, a system containing an aqueous fluid and perhaps minerals remains in equilibrium as its composition, temperature, or both change over the course of a reaction path. Changes in composition can reflect explicit transfer of reactants into and out of the system, and the transfer implicit in buffering gas fugacities and species activities.

Progress along the reaction path is measured arbitrarily in terms of a reaction progress variable ξ, which varies from 0 initially to 1 at the end of the path. Variable ξ, which is dimensionless, has meaning only in terms of how the user has defined the reaction path.

2.2 Example calculation The input file “Feldspar.rea” equilibrates a hypothetical water sample at 25°C and then reacts it with potassium feldspar. Double-click the file, which can be found in the “Scripts” subfolder of the GWB installation directory, to launch React. The Basis pane

describes the composition of the hypothetical water.

Getting Started with React 7

Move to the Reactants pane

to see how potassium feldspar is reacted into the fluid. The following commands

configure the same reaction path. When setting the concentration or activity of species, the mass of minerals, or the

fugacity or partial pressure of gases in the Basis pane, it is important to avoid 0 (zero) values, as these will prevent the GWB programs from solving for the distribution of mass. Where the concentration of a particular component is negligible, set a small positive value. Log values, such as log activity, pH, pe, or Eh, however, can be set to 0.

Na+ = 5 mg/kg K+ = 1 mg/kg Ca++ = 15 mg/kg Mg++ = 3 mg/kg Al+++ = 1 ug/kg SiO2(aq) = 3 mg/kg Cl- = 4 mg/kg SO4-- = 8 mg/kg HCO3- = 50 mg/kg pH = 5 react 400 mg of K-feldspar


Press the Run button on the Results pane to trace the reaction path.

You can alternatively select Run → Go from the menubar or type go in the Command pane.

React produces as output a dataset “React_output.txt” (View Results) that shows calculation results in tabular form, and a dataset “React_plot.gtp” (Plot Results) that passes more complete information to the graphics program Gtplot (see Using Gtplot). Act2 and Tact can project traces of reaction paths on stability diagrams, in which case they also read the “React_plot.gtp” dataset.


The mineralogic results of the reaction, as plotted by Gtplot,

show the results of reacting potassium feldspar into a dilute water at 25°C. The reaction continues until, when about 330 mg of reactant has been added, the fluid reaches equilibrium with K-feldspar.

2.3 Initial system The initial system in a React simulation is an equilibrium model of the aqueous fluid and any coexisting minerals and gases. You constrain the initial system precisely as you would set up an equilibrium model with SpecE8 (see Equilibrium models under Using SpecE8 in the GWB Essentials Guide).

The two programs differ in that React, by default, forces electrical charge balance on the system, whereas SpecE8 does not. To achieve identical output, you should either set SpecE8 to charge balance on the same basis entry as React, or disable charge balancing in React. Specify a basis entry to charge balance on by selecting “Balance species” under the entry’s unit pulldown on the Basis pane,


and disable charge balance by deselecting “Balance species” from the pulldown. You can also disable charge balance from any charged species’ pulldown, not just the current balancing ion, by selecting “Do not balance” from the pulldown. Since React, by default, uses Cl– as the charge balancing ion, this option is especially useful for systems that don’t include any Cl–.


The programs also differ in that React, having figured the distribution of species in the initial system, will by default attempt to find the system’s true equilibrium state by allowing any supersaturated minerals to precipitate. If you do not want the program to take this step, click on Config → Iteration…

and uncheck the box labeled “precipitation”. If you run React on an initial system containing supersaturated minerals, and do not

disable the precipitation option, you should expect two blocks of output in “React_output.txt” (File → View → React_output.txt). Each block contains calculation results, including the concentration of a number of aqueous species, the saturation state of various minerals, the fugacity and partial pressure of gases, and the system’s bulk composition.

If, for example, you run React on the seawater example provided for SpecE8 (the input is given in Equilibrium models under Using SpecE8 in the GWB Essentials Guide), the output dataset will contain two blocks. The top block gives results of the first calculation performed by React. The calculation predicts that seawater is supersaturated with respect to a number of minerals, including antigorite and dolomite. The results in this block, then, represent seawater in a metastable state. The fluid’s bulk composition (but not the concentrations of free species), as well as the CO2 and O2 fugacity, reflect the input constraints.

The program continues to calculate the equilibrium state that seawater, according to the model, would reach if supersaturated minerals were allowed to precipitate. The second block in the dataset gives results of this calculation, which predicts that, at equilibrium, dolomite and quartz coexist with seawater. Precipitating these minerals alters the fluid composition so that the pH and CO2 fugacity reported in the second block differ from the original values.


Finding the true equilibrium state of seawater is a somewhat academic pursuit because mineral precipitation from seawater is too slow to observe. You can tell React to not allow any new minerals to form by turning off the “precipitation” option on the Config → Iteration… dialog, or with the precip off command. In this case, only one block of results would appear in “React_output.txt”.

2.4 Redox disequilibrium React, like the other GWB programs, can account for the redox disequilibrium commonly observed in natural waters. You control the extent to which React honors redox equilibrium when calculating a chemical model by interactively enabling and disabling redox coupling reactions.

See Redox couples in the Introduction to the GWB Essentials Guide for information about decoupling redox reactions, and Redox disequilibrium in the Using SpecE8 section of that guide for specific instructions on constructing disequilibrium models in React.

2.5 Activity coefficients Like SpecE8, React employs various methods for calculating activity coefficients, including: The “B-dot” equation, an extended form of the Debye-Hückel equation. The Harvie-Møller-Weare implementation of the “Pitzer equations”. The activity models implemented in the MINTEQ, PHREEQC, PHRQPITZ, and

WATEQ4F geochemical modeling programs.

For more information, see Activity coefficients in the Using SpecE8 section of the GWB Essentials Guide.


2.6 Sorption onto mineral surfaces React can model the sorption of species from solution onto mineral surfaces, according to several methods (see Sorption onto mineral surfaces in the Introduction to the GWB Essentials Guide). The methods include A two-layer surface complexation model. Ion exchange. Distribution coefficients (Kd ). Freundlich isotherms. Langmuir isotherms.

For more information on applying these methods within React simulations, see Sorption onto mineral surfaces in the Using SpecE8 section of the GWB Essentials Guide.

2.7 Settable variables React allows you to alter the values of certain variables carried in the calculation. Table 2.1 lists these variables and their units and default values. To change a variable, type the new value on the Basis or Medium pane or in the dialog boxes under Config, or enter as a command the variable name followed by the new value. Examples:

The value given must be in the units carried internally by the program, as listed in Table 2.1. To restore a variable to its default value, enter a blank field in the dialog box, or on the Command pane type its name without a value or followed by a ?:

Current values of the variables can be viewed at any time on the relevant dialog box, or using the command show variables.

itmax = 1000 delxi = 5/100

delxi delxi = ?


Table 2.1 Settable variables, their units and default values

Pane or Dialog Variable Default Unit Description

Basis density not set g/cm3 Density of initial fluid.

TDS not set mg/kg Total dissolved solids, initial fluid.

Medium cpw 1 cal/g°C Fluid (water) heat capacity (polythermal mixing).

cpr .2 cal/g°C Mineral (rock) heat capacity (polythermal mixing).

inert 0 cm3 Unreactive volume (porosity calculation).

Output dxplot .005 – Interval in reaction progress between plot points.

dxprint .1 – Interval between printing results.

Iteration epsilon 5 x 10–11 – Convergence criterion.

itmax 400 – Allowed number of iterations, reaction step.

itmax0 999 – Number of iterations, initial system.

nswap 30 – Allowed number of basis changes to find stable mineral assemblage, reaction step.

nswap0 200 – Number of basis changes to find stable assemblage, initial system.

pitz_dgamma 0.1 – For virial activity coefs., maximum fractional change per iteration.

pitz_precon 10 – For virial activity coefs., maximum number of pre-conditioning steps.


pitz_relax 0.5 – For virial activity coefs., relaxation factor during iteration.

simax 3 molal Maximum stoichiometric ionic strength used to calculate water activity (Debye-Hückel model).

timax 3 molal Maximum true ionic strength used to calculate activity coefficients (Debye-Hückel model).

Stepping cpu_max not set s Amount of computing time a simulation may take.

delQ .1 – ΔQ/Q allowed over a step, for kinetic reactions.

delxi .01 – Step size in reaction progress, log/linear stepping.

dx_init not set – Initial step size in reaction progress.

step_increase 1.5 – Maximum proportional increase in step size.

step_max not set – Number of reaction steps the program may take to trace a simulation.

theta .6 – Time weighting for tracing kinetic rate laws.


2.8 Controlling the printout React lets you control the amount of detail presented in the calculation results written to “React_output.txt”. The dataset is known commonly as the “printout”, although it need never be printed. The printout can contain information about (1) the concentration and activity of dissolved species, (2) the saturation indices of various minerals, (3) gas fugacity and partial pressure, (4) surface complexes, and (5) the elemental composition of the fluid, mobile colloids, stagnant zone, and bulk system, (6) those compositions expressed in terms of either the current or original basis, and (7) the diffusion profile within the stagnant zone. The printout can also contain a list of the chemical reactions considered in the calculation.

You can specify that any of these lists be excluded from the printout or included in a short or long format. The program, by default, produces lists of dissolved species and mineral saturation states in a short format, which includes only species present in concentrations greater than 10–8 molal and minerals with saturation indices greater than –3. The fugacity and partial pressure of each gas appears in the printout, as does composition in terms of elements and the original basis.

To vary the printout, the user can set each aspect in Table 2.2 to “none”, “short”, or “long” on the Config → Output… dialog


or in a command. For example,

The current print settings can be viewed at any time by looking at the three-way check boxes on the Config → Output… dialog. A blank check box indicates exclusion from the printout, a check indicates inclusion in short format, and shading indicates inclusion in long format. Alternatively, type

Table 2.2 Print options and default settings in React

Option Default Description

print dataset on To “React_output.txt”

print alphabetically off Arrange entries in dataset alphabetically

species short Aqueous species

surfaces long Surface complexes

saturations short Mineral saturation states

gases long Gas fugacities

basis none Composition, current basis

orig_basis long Composition, original basis

elements long Elemental composition

reactions none Chemical reactions

stagnant none Composition of stagnant zone

print species = long print saturations = none

show printout


2.9 React command line You can start React by clicking the icon under the “Start” menu, opening a “.rea” file, or entering the command react.exe from the Windows “Command Prompt”.

When you start React from the command line (as opposed to clicking on the icon), you can specify a number of arguments. For example, the command

causes React to read input commands from a file “my_script”, and to use “my_thermo.tdat” as the thermodynamic database.

The following options are available from the command line: -cd Change the working directory to the directory

containing the input script specified with the –i option.

-nocd Do not change the working directory.

<input_script> -i <input_script>

Set a file from which to read input commands.

-gtd <gtdata_dir> Set directory to search for thermodynamic datasets.

-cond <cond_data> Set the dataset for calculating electrical conductivity.

-d <thermo_data> Set the thermodynamic dataset.

-iso <isotope_data> Set the dataset of isotope fractionation factors.

-s <surface_data> Set a dataset of surface sorption reactions.

react –i my_script –d my_thermo.tdat

19

Tracing Reaction Paths

React can trace several types of reaction paths, including Titration paths, in which a reactant is gradually added to a geochemical system. Polythermal paths, in which temperature varies. Sliding paths, in which a species activity or gas fugacity varies. Kinetic paths, in which the rate of reaction progress is described by a kinetic rate

law.

These types of paths can be combined into a single React simulation. This section of the guide describes how to construct the first three types of reaction

paths, and the following two sections give details on constructing kinetic reaction paths.

3.1 Titration paths In simple reaction paths, one or more reactants are gradually added to (or removed from) the system over the course of the calculation. Such paths are sometimes called “titration paths” because the program repeatedly adds a small aliquot of reactant and then recalculates the system’s equilibrium state as it steps forward in reaction progress. Other methods of varying the system composition, such as buffered paths, sliding fugacity and activity paths, and kinetic paths, are discussed in later sections of this manual.

In the following example, the program simulates reaction of an alkaline industrial waste that has been pumped into an injection well with a dolomite formation receiving the waste. Double-click on file “Dolomite.rea” (the file can be found in the “Scripts” folder within the GWB installation directory), and when React opens, look at the Basis pane,


which contains the composition of the alkaline waste. You don’t need to constrain the concentration of Na+ because it’s selected as the charge balancing ion.

If the fluid composition wasn’t already set, you would do so by clicking the button to add entries to the basis, then select units from the pulldown for each entry and constrain their values. To set Na+ as the charge balancing ion, select the “Balance species” option from its unit pulldown.

Move to the Reactants pane.

The input sets up the irreversible reaction of dolomite into the NaOH-NaCl waste. If the titration path isn’t already set up, you can do so by going to → Simple → Mineral… → Dolomite and specifying the amount to react.

Tracing Reaction Paths 21

You could also have used the commands

The initial commands correspond to the settings on the Basis pane, while the final step matches the input to the Reactants pane.

In the example, the program reacts 50 cm3 of dolomite over the reaction path. If the program takes 100 reaction steps of Δξ = .01, then a half cm3 of dolomite is added to the system at each step. As can be seen in the calculation results,

dolomite reacts with the fluid to form calcite and brucite until the fluid becomes saturated. Reaction stops at this point, so that any dolomite further added to the system simply accumulates.

Aqueous species and gases, as well as minerals, may serve as reactants in titration paths. Reactant quantities can be set in a variety of units, listed in Table 3.1.

T = 50 pH = 13 Cl- = 3 molal Ca++ = 1 mg/kg HCO3- = 1 mg/kg Mg++ = 1 mg/kg balance on Na+ react 50 cm3 Dolomite go


Table 3.1 Units for specifying reaction rates

By amount to add over the reaction path:

mol, mmol, umol, nmol

kg, g, mg, ug, ng

cm3

eq, meq, ueq, neq

mol/kg, mmol/kg, umol/kg, nmol/kg

molal, mmolal, umolal, nmolal

mol/l, mmol/l, umol/l, nmol/l

g/kg, mg/kg, ug/kg, ng/kg, wt fraction, wt%

eq/kg, meq/kg, ueq/kg, neq/kg

eq/l, meq/l, ueq/l, neq/l

mol/cm3, mmol/cm3, umol/cm3, nmol/cm3

kg/cm3, g/cm3, mg/cm3, ug/cm3, ng/cm3

mol/m3, mmol/m3, umol/m3, nmol/m3

kg/m3, g/m3, mg/m3, ug/m3, ng/m3

volume%, vol. fract.

By absolute rate (append):

/s, /min, /hr, /day, /yr, /m.y.

As many reactants as desired can be specified: click → Simple on the Reactants

pane, or use a react command for each. If multiple reactants are set, the program adds each to the system at a rate in proportion to its total mass.

The role of reactants is to change the system’s composition. For this reason, only the reactant’s composition is important. Quartz, for example, could be replaced as a reactant by the silica polymorph tridymite or even SiO2(aq) without affecting the calculation results.


For an example of a titration path accounting for an ion exchange reaction, double-click on file “IonEx.rea”. When it opens, go to the Basis pane,

which describes a fluid containing Ca++ and Na+. Load an exchanging surface into the program by going to File → Open → Sorbing

Surfaces… and add the “IonEx.sdat” dataset from the “Gtdata” folder within the GWB installation directory.

The dataset contains selectivity coefficients for exchange between Ca++ and Na+.


Move to the Reactants pane,

where the program is configured to titrate NaCl into the initial system. In this example, the Na+ added to the solution drives an ion exchange reaction that liberates Ca++ from the exchanging surface.

To use a fluid as a reactant, you must determine the fluid’s bulk composition by calculating an equilibrium model. Each component in the fluid appears on a separate line. After defining the initial system, the Reactants pane might look like

React provides a convenient method to take the fluid composition resulting from an equilibrium model and use it as a reactant, without reentering the reactant’s composition as done here (see Picking up the results of a run, later in this section).


React normally adds reactants at rates that remain constant over the path, but a cutoff value may be set on the Reactants pane (click next to the reactant in question), or with the react command. The input

or the equivalent steps

cause a half gram of quartz and albite to be reacted. The program adds quartz continuously over the path, whereas it reacts albite twice as quickly as quartz over the first half of the path and not at all over the second.

A final feature of React is the “dump” option. When this option is set, the program removes any minerals present in the initial system before beginning the reaction path. The option is useful for simulating separation of a fluid from a rock with which it was in equilibrium, before beginning a path. For example, you may want to separate a geothermal fluid from the reservoir rocks before modeling how the fluid could react to form scale. Set the option from the Config → Stepping… dialog or by typing dump.

(define an initial system) react 1/2 g Quartz react 1 g Albite cutoff = 1/2


Unchecking “dump” or using the dump off command turns off the option.

3.2 Flow-through model React features a “flow-through” model in which minerals are prevented from dissolving once they precipitate. The model is useful for modeling reaction of a packet of fluid as it migrates through an aquifer. Once minerals form, they are isolated from the packet so that they cannot back-react with the fluid should they become undersaturated farther along the flow path. Implement the flow-through model from the Config → Stepping… dialog, or by typing flow-through.

To turn the model off, uncheck “flow-through” or type flow-through off. The flow-through model can be applied to a variety of problems in which minerals are

unlikely, for physical or chemical reasons, to dissolve once they form. To simulate


evaporation of seawater, for example, the model provides a way to account for the settling of minerals to the sea floor. Double-click the “Evaporate.rea” input file to launch React.

The Harvie-Møller-Weare activity model is specified to account for the high ionic strength of evaporated seawater. If not already loaded, you could do so by going to File → Open → Thermo Data… and selecting “thermo_hmw.tdat”. You can view the contents of the dataset by going to File → View → .\thermo_hmw.tdat.

The Basis pane

defines the model of surface seawater. Move to the Reactants pane.


H2O is set as a simple reactant with a negative mass, so over the reaction path the program removes nearly all the solvent water from the system.

On the Config → Stepping… dialog, the value specified for “delxi” (see Settable variables in the section Getting Started with React) causes the program to take reaction steps ∆ξ that are smaller than the default.

The flow-through setting, as described above, has been applied to simulate fractionation of the precipitating minerals. Click OK.


On the Config → Output… dialog, setting “dxplot” to 0 causes each reaction step to be written to “React_plot.gtp”. Click OK.

Note that React carries the reaction path to the point of near complete desiccation, at which point it abandons any attempt to further trace the path; the “error” message produced is expected behavior and can be ignored. The calculation results show the sequence of minerals that precipitate during the evaporation of seawater at 25°C.


3.3 Flush model A flush model is a special reaction path in which a fluid, added as a reactant, displaces existing fluid from the system. In contrast to the reference frame of a flow-through model, which follows a migrating fluid, a flush model is traced from the reference frame of the rock through which the fluid migrates. Set a flush model from the Config → Stepping… dialog, or type the command flush.

To turn off the option, uncheck “flush” or type the command flush off. To simulate, for example, reaction in a quartzite containing muscovite and microcline

as CO2-charged fluid migrates through it, double-click the “Flush.rea” input file. When React opens, go to the Basis pane.

The input describes the initial mineralogy and pore water fluid of the quartzite.



which sets the CO2-charged water to be reacted into the system. Because of the value set for “reactants times”, 100 kg of fluid will be reacted.

On the Config → Stepping… dialog,

the “flush” option has been selected. As a result, the reactant fluid will displace an equal amount of fluid (in terms of water mass) from the system.


3.4 Polythermal reaction paths React traces polythermal reactions in one of three ways. It can vary temperature linearly from an initial to a final value over a reaction path—such a calculation is called a “sliding temperature” path. The program can also calculate temperature from the mixing of reactants at one temperature into an initial system of another, assuming approximate values for heat capacity. This second option is called a “polythermal mixing” or “quench” model. Finally, the program can account for heat produced or consumed internally in the domain, as described in the Internal heat production section of the GWB Reactive Transport Modeling Guide. A heat source can be applied in a “normal” path in which you only set the initial temperature of the system, or in conjunction with a “polythermal mixing” path, but not with the “sliding temperature” option. Polythermal paths can trace the simple heating or cooling of a chemical system, or can be combined with other React features, such as reactants, kinetic rate laws, and isotopic fractionation.

To set a sliding temperature model, specify initial and final temperatures in the range of the thermo data, typically 0°C–300°C. For example, to simulate cooling, set the system’s composition in the usual way and enter the beginning and ending temperatures: click the pulldown next to the unit for temperature on the Basis pane, then choose “sliding temperature”.

Upon selecting this option, “temperature” will be relabeled “initial temperature” and a new field labeled “slide temperature to” will appear below it.

In this case, the system begins at 300°C and cools to 25°C. Alternatively, set the sliding temperature path with the command

temperature initial = 300, final = 25


In a polythermal mixing model, set the temperatures for the reactants and the initial system. Over the path, the program calculates the temperature from the mass of reactant that has been added to the system, using the approximate heat capacities for fluids (water) and minerals (rock) stored in variables “cpw” and “cpr” (set on the Medium pane; see Settable variables in the section Getting Started with React). To set the polythermal mixing model, choose “reactant mixing” from the pulldown, then set a value for the “reactant temperature” field that appears.

In the following example, the program is applied to model a steam flood of a hypothetical petroleum reservoir composed of quartz, illite (muscovite), albite, and (ordered) dolomite. The “steam” here is actually hot water containing CO2. Double-click on the “Steam.rea” input file. When React opens, go to the Basis pane,


which sets the composition of the formation and initial fluid, as well as the temperature of the reactant fluid and initial system.


where the composition of the reactant fluid is defined. On the Config → Stepping… dialog,


the “flush” option has been enabled. This setting, combined with the value set for “reactants times” on the Reactants pane, causes the hot reactant fluid to pass through the initially cooler formation 20 times.

The figure below shows the calculation results.

The reservoir, initially at 60°C, is progressively heated as the 200°C flood passes through. The horizontal axis represents the number of times the 1 kg of pore water in the system is replaced.

3.5 Buffered paths React can trace reaction paths in which one or more species activities or gas fugacities are held constant. Values of pH, Eh, and pe may also be fixed. Fixed activity and fixed fugacity paths provide a means of modeling systems buffered in nature by contact with a gas reservoir such as the atmosphere, or in the laboratory by a pH-stat or similar device.

To model a buffered system, fix an activity or fugacity from the Reactants pane: click on → Fixed, then select the desired option. Selecting Aqueous… or Gas… will bring up a pulldown of species to choose from.


You can also set a buffered path by typing a command such as

or

In these cases, the program maintains the fluid’s CO2 fugacity and pH at their initial values. To simulate pyrite dissolving into a water that remains oxidized by contact with the

atmosphere, double-click on the “Pyrite.rea” input file. When React opens, go to the Basis pane

fix f CO2(g)

fix pH


to see the initial composition, which is set to be in equilibrium with O2(g) in the atmosphere.

On the Reactants pane,

the fixed O2(g) fugacity buffer ensures that the water remains oxidized as Pyrite is titrated into the fluid.

To hold an activity ratio constant over the course of a reaction path, “fix” the ratio on the Reactants pane by clicking on → Fixed → Ratio…

then choosing species, and their powers, for the numerator and denominator. For example, the setting below


or the equivalent command

holds invariant the activity ratio for calcium and sodium ions to reflect a simple ion exchange buffer.

3.6 Sliding activity and fugacity React cannot only hold species activities and gas fugacities constant, but can vary one or more of these values over a reaction path. Calculations of this type are known as sliding activity paths and sliding fugacity paths. To set a sliding activity or fugacity, move to the Reactants pane and choose → Sliding, or use the slide command.

To calculate the effect at 60°C of CO2 escaping from a groundwater in equilibrium with calcite, for example, double-click on the “Degas.rea” input file. The Basis pane

defines a groundwater in equilibrium with calcite.

fix ratio Ca++/Na+^2


Move to the Reactants pane

to set the sliding fugacity path, or use the command

The CO2 fugacity in this example slides linearly from its initial value of about 35 to 1 at the end of the path. If, on the other hand, you had specified log units on the Reactants pane

or with the command

the program would have varied the logarithm of the CO2 fugacity linearly from its initial to final value.

slide f CO2(g) to 1

slide log f CO2(g) to 0


The figure below shows calcite precipitated over the course of CO2 degassing at 60°C, as simulated by the sliding fugacity path.

As a second example, calculate the species distribution of uranium(IV) versus pH by sliding pH from 2 to 12. Double-click on the “Uranium.rea” input file and, when React opens, move to the Basis pane,

which sets up the initial system: a fluid containing uranium with a pH of 2. Note that the program maintains electrical neutrality over the path by varying the Cl– concentration.



the sliding pH path is implemented. The program will vary pH from its initial value of 2 to the target value of 12.

The figure below shows the distribution of uranium(IV) species as a function of pH, calculated as a sliding activity path.

As a final example, compute the effect of pH on surface complexation. Double-click on the “Surface.rea” input file. When React opens, go to the Basis pane to see the initial fluid composition.


Here, Fe(OH)3(ppd) serves as a proxy for hydrous ferric hydroxide. Load the Dzombak and Morel dataset for ion complexation with hydrous ferric oxide by

going to File → Open → Sorbing Surfaces… and adding the “FeOH.sdat” dataset.


On the Config → Iteration… dialog,

the “precipitation” option has been deselected. As a result, the more stable ferric oxide minerals are prevented from forming.

The Reactants pane

sets up the sliding pH path. The calculation results, shown below, show sorption as a function of pH of various components from solution onto a hydrous ferric hydroxide surface.


Running the simulation produces the result

You can vary an activity ratio over the course of a path in a similar fashion. Choose on the Reactants pane → Sliding → Ratio…

then set the species in the ratio and their powers.


Alternatively, use the command

3.7 “Flash diagrams” You can use React to calculate “flash diagrams” of the type employed by reservoir engineers to study scaling. A flash diagram shows the mineral masses that precipitate, or the saturation state of various minerals, when two fluids are mixed in varying proportions. The diagrams do not represent “flashing” in the geochemical sense of gas escaping from a fluid.

In calculating a flash plot, React gradually removes the original fluid from the equilibrium system as it titrates in a reactant fluid. Enable the feature from the Config → Stepping… dialog

by selecting the “fluid” option from the flash pulldown, or by typing flash. Disable it by selecting “off” from the pulldown, or with the command flash off.

Selecting “system” from the flash pulldown, or typing flash system

removes the initial system, including fluid and minerals.

slide Ca++/Na+^2 to .01


For example, the input script “Flash.rea” traces a reaction path representing the mixing of two fluids in all possible mixing ratios. Double-click the file to launch React, then move to the Basis pane,

where a fluid rich in barium, but depleted in sulfate, is defined. The Reactants pane contains a reactant fluid rich in barium but with little sulfate.


The reactant fluid was originally entered on the Basis pane, equilibrated (Run → Go), then “picked up” and moved to the Reactants pane (Run → Pickup → Reactants → Fluid). The “pickup” command is explained in the section Picking up the results of a run, later in this chapter.

On the Config → Stepping… dialog,

the flash option is enabled.


You could have instead used the commands

Run → Go traces the simulation. Using Gtplot, you can plot the mineral mass produced versus extent of mixing.

T = 120 Na+ = 27000 mg/kg Cl- = 42000 mg/kg SO4-- = 1 mg/kg Ba++ = 400 mg/kg pH = 5.8 go pickup reactants = fluid Na+ = 10800 mg/kg Cl- = 15500 mg/kg SO4-- = 2000 mg/kg Ba++ = 100 ug/kg pH = 6.5 flash = on go


The horizontal axis shows the extent of mixing from purely the first fluid (left) to purely the second (right); a mixing value of 0.4, for example, represents a mixture of 60% of the first fluid and 40% of the second.

By disabling precipitation in the React run (on the Config → Iteration… dialog,

or by typing precip = off), you can plot mineral saturation states.

3.8 Fractionation of stable isotopes As described in the Fractionation of stable isotopes section of the GWB Essentials Guide, the reaction modeling programs in the GWB can account for the equilibrium fractionation of stable isotopes. The GWB is distributed with a database “isotope.dat” containing fractionation factor correlations for the isotopes 2H, 13C, 18O, and 34S. You can augment the database by adding isotopes such as 17O of those elements, or isotopes like 57Fe of other elements.

Program React can trace the equilibrium fractionation of stable isotopes over the course of a reaction path. To define an isotopic path, set first the fluid’s initial composition and then the isotopic composition of whatever reactants are to be added to the system. You set the isotopic compositions from either the Config → Isotopes… dialog or the Command pane.


To trace oxygen fractionation as a system reacts with quartz, for example, begin by adding “Quartz” as a reactant, then enter values for δ18O of the initial fluid as well as the reactant mineral

Alternatively, type the command

You may specify compositions relative to any isotopic standard, including SMOW, PDB, or CDT. The program predicts over the reaction path isotopic compositions for species, minerals, and gases relative to the same standard, and writes the results to the dataset “React_isotope.txt”, as well as to “React_plot.gtp”, where it is available for plotting by Gtplot.

The program begins by calculating the compositions of solvent and dissolved species to honor the fluid’s bulk composition, as specified, assuming isotopic equilibrium among species. The program then sets minerals in the initial system and any buffered gases to compositions in equilibrium with the fluid.

Adding or removing reactants over the course of a reaction path changes the system’s isotopic composition. The program responds by redistributing isotopic mass to maintain equilibrium among solvent, aqueous and surface species, and minerals. You specify the compositions of reactants that are added to the system. When reactants are removed, however, the program assumes the composition of the reactant species as it exists at that point in the reaction path.

The calculation as described treats minerals as if they exchange isotopes rapidly enough to remain in equilibrium with the changing system. This assumption, which can be unrealistic, may be relaxed by specifying that a mineral, or some fraction of the mineral’s mass, remain segregated from isotopic exchange.

oxygen initial = -5, Quartz = +40


A segregated mineral changes composition over a reaction step when it precipitates from solution; the newly precipitated mineral forms in isotopic equilibrium with the system, but any of the mineral present at the start of the step is unaffected. Conversely, a segregated mineral affects the system’s composition when it dissolves. Note that a kinetic mineral exists outside the equilibrium system and hence behaves isotopically as if it were a fully segregated mineral.

To hold a mineral segregated, move to the Config → Isotopes… dialog and select the mineral by clicking . For example, you could segregate muscovite and assign its composition at the start of the path as shown below (Note you must set the initial bulk fluid composition for an isotope system before you can use the GUI to set the composition of reactants or segregated minerals in that system).

Alternatively, type the commands

If you do not specify a segregated mineral’s composition, and it is present in the initial system, the program will set its composition to be in equilibrium with the initial fluid.

segregate Muscovite oxygen Muscovite = +30 hydrogen Muscovite = -20


Table 3.2 Isotopic composition of reactants

Reactant Mass is being added Mass is being removed

Simple reactant

Set by modeler

For existing mineral, its segregated plus unsegregated composition; else, composition in equilibrium with current fluid

Fixed or sliding buffer

Set by modeler; defaults to equilibrium with initial system (ξ = 0)

Isotopic equilibrium with fluid at current point in reaction path

Kinetic mineral

Set by modeler, unless dissolving mineral is completely within the equilibrium system at ξ = 0, in which case the mineral’s segregated plus unsegregated composition

Increment in mass of precipitating mineral is in isotopic equilibrium with current system; bulk reactant composition reflects cumulative mass to current point in reaction path

Kinetic gas transfer

Set by modeler; defaults to equilibrium with initial system


Charge rebalancing

Set by modeler; defaults to equilibrium with initial system


React treats buffered reactants in a manner similar to simple reactants. When added, a

buffered species or gas assumes the composition specified by the modeler, or, by default, the composition in equilibrium with the initial system. Upon removal, the buffer takes on the composition in equilibrium with the system at the current point in the reaction path. Table 3.2 summarizes how React assigns isotopic compositions to various types of reactants as it traces a reaction path.

React treats flush and flash models in the same way: you specify the isotopic composition of each component in the flushing or flashing fluid. In a flow-through model, the program reports the isotopic composition of the increment in mineral mass precipitated over the current step, rather than the composition of the cumulative mass.


Consider, as an example, the effects of pyrite dissolving into a groundwater that remains oxidized by contact with the atmosphere. Double-click on the “Isotope.rea” input file to launch React. The Basis pane

describes the initial groundwater, an oxygenated fluid in equilibrium with calcite and hematite.


pyrite is reacted into the oxygenated system. As a result, calcite will dissolve and gypsum will precipitate.


On the Config → Isotopes… dialog,

specify the isotopic composition of the initial fluid, the reactant mineral pyrite, and calcite. Calcite, which is in chemical equilibrium with the water, is segregated isotopically.

The 18O and 34S composition of the resulting gypsum reflects the influence, respectively, of the calcite and pyrite compositions. The fluid’s 13C composition varies from its initial value toward that of the calcite, and its 34S value decreases toward the pyrite composition.


Mass Reacted, Pyrite (cm3)


3.9 Picking up the results of a run React has the ability to “pick up” the results of a calculation and use these results as the starting point for a new calculation. You can pick up an entire system or just the fluid or mineral fraction, and use these results as a new equilibrium system or a new set of reactants. Choosing from the menubar Run → Pickup → System → Entire,

dragging the Results pane onto the Basis pane, or issuing the command

for example, picks up fluid and any coexisting minerals as a new equilibrium system. Run → Pickup → System → Fluid

pickup


or the command

picks up only the fluid, whereas Run → Pickup → Reactants → Minerals,

or the command

picks up the resulting minerals as a set of reactants. You can use the pickup feature, as an example, to simulate the mixing of two fluids. To

mix fluid 1 (whose composition, pH, etc. are listed in dataset “Fluid1”) into fluid 2 (in dataset “Fluid2”), follow the steps

React equilibrates fluid 1 and takes the fluid’s bulk composition as a reactant. The program then equilibrates fluid 2 and reacts about 10 kg of fluid 1 into the second fluid over the course of a reaction path.

pickup fluid

pickup reactants = minerals

read Fluid1 go pickup reactants = fluid read Fluid2 reactants times 10 go


The pickup command also allows you to pick up kinetic reactions at their endpoint states, and thus chain together kinetic reaction paths. This feature is discussed in Chaining together kinetic paths in the next chapter of this guide.

59

Kinetic Reaction Paths

In the reaction models discussed to this point, reactants are added to (or removed from) a system at arbitrary rates. React can also trace reactions in which kinetic rate laws control the time rates at which reactions proceed.

React can trace the progress through time of several types of kinetic reactions, including

The dissolution and precipitation of minerals. The dissociation and association of aqueous complexes, or surface complexes. The transfer of gases from an external reservoir, or into one. Oxidation and reduction (redox) reactions, in solutions held in redox

disequilibrium. The rate of microbial metabolism and the growth of microbial communities.

You can construct a model considering a single kinetic reaction, or one combining several reactions or types of reactions. Kinetic modeling is discussed in detail in the remainder of this section.

4.1 Setting kinetic reactions To construct a kinetic reaction path, specify the time span of the simulation on the Basis pane, or with the time command. Then set one or more kinetic reactions, either on the Reactants pane (click and the appropriate option) or using the kinetic command. In this way, you define the specifics of the rate law, such as the rate constant to be used, reaction orders, and so on. Table 4.1 summarizes the keywords that can be used to define kinetic reactions.


Table 4.1 Summary of keywords for the kinetic command. Symbol ✓ indicates that for the applicable reaction types, a value for the keyword must be set. For symbol *, note the following: (1) an activation energy and a pre-exponential constant can be specified in place of a rate constant; (2) a value for surface must be set for redox reactions considering a heterogeneous catalyst; (3) a value for KA is required for enzymatically promoted reactions; and (4) a value for mE or aE is required when modeling enzyme kinetics. For symbol †, note: (1) units shown for rate_con and pre-exp are in the absence of promoting and inhibiting species, as set with apower or mpower keyword; (2) units for KA and KD depend on settings for mpowerA and mpowerD. Use keywords apower, apowerA, and apowerD to set a species’ activity in rate law, and mpower, mpowerA, and mpowerD to set its molality.

reaction type

keyword mineral complex gas redox microbe default unit

rate_con • • ✓ mol/cm2 sec†

• • ✓ molal/s or molal/cm2 sec†

• ✓ mol/mg sec†

pre-exp • • • • • * same as rate_con

act_en • • • • • * J/mol

surface, contact

• • ✓ cm2/g

• * cm2/g or cm2

apower, mpower • • • • • none set

order1 • • • • • 1

order2 • • • • • 1

xaffin • not set

nucleus • 0 cm2/ cm3

critSI • 0

f_ext • equilib’m fugacity

p_ext • not set bar

Kinetic Reaction Paths 61

rxn • • ✓

catalyst • off

mE, aE • * molality or activity

KA • * molality or activity

KP • not set molality or activity

KA • 0 †

KD • 0 †

ATP_energy • 0 kJ/mol

ATP_number • 0

biomass • ✓ mg/kg

PKA • 1

PKD • 1

apowerA, mpowerA

• none set

apowerD, mpowerD

• none set

growth_yield • 0 mg biomass/mol

decay_con • 0 sec–1 The rate law for each type of kinetic reaction is coded within React in a form

sufficiently general to support most applications in geochemistry. This form is the “built in” rate law. You may, furthermore, specify the form of a rate law directly. React evaluates the rate law you set using an internal interpreter. For example, after adding the kinetic mineral quartz from the Reactants pane, you could change the rate law pulldown from “built in” to “equation” and then set the form directly, as in the box below.

The equation prescribes a rate law of the form shown, for the dissolution and precipitation of quartz. On the Command pane, you would type


You can also write basic scripts to calculate reaction rates, and even write and compile C++ functions that React links to and executes at run time. Methods for setting custom rate laws are described in detail in the next section of this guide, Custom Rate Laws.

At each point in a simulation, React selects a time step short enough to accurately trace each kinetic reaction considered, and to ensure numerical stability. Introducing kinetic rate laws can sometimes lead to lengthy runs, for this reason, if the time span of the simulation is long relative to the characteristic times of the kinetic reactions considered. Calculating a simulation spanning millions of years, for example, might require a lot of computing time if the run includes kinetic reactions that approach equilibrium within a few days.

To constrain a time step, the program allows only a small change in the relative value of the ion activity product (i.e., in ∆Q/Q) for each kinetic reaction. The limiting projected change in this quantity is by default 0.1, but you can set your own criterion, as described below. Setting a value larger than the default can lead to longer time steps, whereas a smaller value might improve stability by forcing smaller steps. You can also constrain the time step directly by adjusting the variable “delxi”.

A time weighting variable 𝜃𝜃, which can range from 0 to 1, controls the method React uses to integrate rate laws. When 𝜃𝜃 is 0, the integration proceeds by evaluating reaction rates only at the start of each time step, whereas a θ value of 1 causes the rates to be figured at the step’s end, as part of the Newton-Raphson iteration. Prescribing an intermediate value sets a weighted average of the rates, before and after. Values close to one-half give runs that are more stable numerically than when 𝜃𝜃 = 0, and lead to less truncation error than when 𝜃𝜃 is either 0 or 1. In React, the default value is 0.6.

Values “delQ”, “delxi”, and “theta” are examples of “settable variables,” as described under Settable variables in the Getting Started with React section of this guide. You can alter these values directly from the command line or using a script, or on the Config → Stepping… dialog. To constrain the time stepping tightly, for example, you might reduce the value for “delQ” by a factor of 10 by changing the value to 0.01

kinetic Quartz rate_law = “rate_con * surface * (1 – Q/K)”


or type delQ = 0.01. The command show variables lists the settable variables and their current values.

4.2 Kinetics of precipitation and dissolution A simple rate law for mineral dissolution and precipitation takes the form

r k→ = ASk+ �1− 𝑄𝑄K� (4.1)

Here r k→ is reaction rate (mol/s, positive for dissolution), AS is the mineral’s surface area

(cm2), k+ is the rate constant (in mol/cm2 sec), and Q and K are the activity product and

equilibrium constant for the dissolution reaction. By this equation, a mineral precipitates when it is supersaturated and dissolves when it

is undersaturated at a rate that depends on its rate constant and surface area. React calculates surface area from a specific surface area in cm2/g entered by the user for each kinetic mineral. The user also supplies the value of the rate constant, or an activation energy EA and pre-exponential factor A for the Arrhenius equation


k+ = A e−EA RTK⁄ (4.2)

so that the program can determine k+ as temperature varies. Here, R is the gas constant and TK is the absolute temperature in Kelvins. There is provision in React for more complicated rate expressions than the rate law above, such as those in which the rate law accounts for promoting and inhibiting species in solution, as discussed later.

You can set kinetic rate laws for minerals swapped into the initial system and thus initially in equilibrium with the fluid, as well as for minerals set as reactants. However, a kinetic mineral must exist in some amount (or a nucleation term must be set, as described below); otherwise, its surface area will be 0 and it will never precipitate.

As an example, trace the kinetic dissolution of albite at 70°C into a water in equilibrium with kaolinite, muscovite, and quartz, assuming that the reaction of quartz is also controlled kinetically. Open “Kinetic.rea” and move to the Basis pane.

Swapping kaolinite, muscovite, and quartz into the basis sets the 70°C fluid in equilibrium with the minerals. Set a time span of 1500 years.


On the Reactants pane, expand the “Kinetic” fields for the two minerals.

Rate constants of 10–15 and 2 × 10–16 mol/cm2/sec are set for albite and quartz, and a specific surface area of 103 cm2/g is set for each mineral.

If working from the Command pane, type

T = 70 swap Kaolinite for Al+++ swap Quartz for SiO2(aq) swap Muscovite for K+ pH = 6 Na+ = .3 molal Ca++ = .05 molal Cl- = .3 molal HCO3- = .02 molal 10 free g Kaolinite 100 free g Quartz 10 free g Muscovite


Run → Go traces the simulation. The results

show that albite reaches equilibrium twice in the calculation, once in the presence of tridymite and again in the presence of quartz.

(cont’d) react 25 g "Albite low" kinetic "Albite low" rate_con = 1e-15 surf = 1e3 kinetic Quartz rate_con = 2e-16 surf = 1e3 time begin 0 yr, end 1500 yr go


4.2.1 Promoting and inhibiting species The kinetic rate law carried to this point can be generalized to account for the effects of promoting and inhibiting species. In this case, the law takes the form

r k→ = AS k+ ��aj�mj�𝑝𝑝j

j

�1 − QK� (4.3)

Here ∏ is the product function (the multiplicative equivalent of the summation function ∑), aj and mj are the activity and molality of each promoting or inhibiting species (the notation “aj/mj” signifies that either the species activity or molality is carried), and pj is that species’ “power” in the rate law.

A promoting species has a positive value for pj, and an inhibiting species has a negative value. When there are no promoting or inhibiting species, this rate law reduces to the previous form. Aqueous species, minerals, gas species (represented in the rate law by fugacity or partial pressure), surface complexes (represented by the species’ molality), and solvent water can serve as promoting and inhibiting species.

To set the promoting and inhibiting species in a rate law, click the button within the “power” section of the kinetic reactant and choose a species from the pulldown list.

Set a value for the “power” (the default is 1), then choose whether the species activity

or molality should be evaluated in the rate law by selecting the appropriate button.

From the Command pane, use the apower or mpower (also apow or mpow) keyword within the kinetic command to set the species activity or molality, respectively, in the rate law. For a gas species, keywords fpower and ppower set the term as fugacity or partial pressure, in bar. The generic keyword power sets the solvent or an aqueous species in terms of activity, a gas as fugacity, and a surface species in terms of molality.


As an example, open “Albite.rea” and move to the Basis pane,

which defines an acidic fluid at 70°C. The simulation will span 30 days. The kinetic rate law for albite dissolution is set on the Reactants pane,


Or, type

The rate law assumes that H+ acts as a promoter, the activity of which is raised to a power of one. The example includes a single promoting species, but you can set for each rate law as many promoting and inhibiting species as you desire.

time begin = 0 day, end = 30 day T = 70 pH = 1.5 0.1 molal Cl- 0.1 molal Na+ 1 umolal SiO2(aq) 1 umolal Al+++ react 250 g of "Albite low" kinetic "Albite low" rate_con = 6.3e-13, apower(H+) = 1 kinetic "Albite low" surface = 1000 fix pH go


4.2.2 Nonlinear rate laws React can also treat rate laws of the nonlinear form

r k→ = sgn �1− QK� AS k+ ��aj�mj�

𝑝𝑝j

j

�1 − �QK�𝜔𝜔�Ω

(4.4)

Here, sgn is a function returning −1 or +1, depending on the sign of its argument, and

variables ω and Ω are the “orders” of the rate law, which define the nonlinearity. When both orders are set to 1, the form of the rate law reduces to the previous form.

Set 𝜔𝜔 and Ω with keywords “order1” and “order2”. As an example, open “Nonlinear.rea”. The Basis pane

sets the initial fluid composition and the timespan of the simulation. The Reactants pane


describes the dissolution of quartz at 100°C, taking a value of 2 for ω and 1 for Ω.

4.2.3 Cross-affinity rate laws React supports the use of “cross-affinity” rate laws, in which the saturation state (i.e., Q/K) of one mineral is used to calculate the reaction rate of another mineral. Rate laws of this form are useful for studying problems such as glass dissolution, where reaction of an altered surface layer appears to control the overall dissolution rate.

To set the cross-affinity option, choose a mineral from the pulldown next to “xaffin”.


For a purely hypothetical example, the cross-affinity setting in tridymite’s rate law below

causes the program to calculate the reaction rate of tridymite according to the fluid’s saturation state with respect to the mineral cristobalite. Alternatively, type

Selecting “off”

or typing

turns off the option.

4.2.4 Nucleation You can set for any kinetic mineral a simple description of nucleation. This feature allows minerals not present in the chemical system to form according to kinetic rate laws. In the absence of a treatment for nucleation, a new kinetic mineral would not be able to form

kinetic Tridymite xaffin = Cristobalite

kinetic Tridymite xaffin = OFF


because its surface area AS would be 0, leading to null reaction rates according to the rate laws.

To set the surface area (in cm2/cm3 fluid volume) available in the chemical system for nucleation whenever a mineral is supersaturated, enter a value for “nucleus density” in the kinetic rate law for that mineral.

This option prescribes a minimum value for a supersaturated mineral’s AS over the calculation. For example, the setting below

or the command

prescribes that, per cm3 of fluid, 100 cm2 of surface area is available for the growth of quartz. By default, the nucleation area is 0.

In addition, you can set a critical saturation index (log Q/K) for a mineral. In this case, the mineral’s nucleation area is available only when its saturation index exceeds the prescribed value. Set this option using “critical saturation index”

or the CritSI keyword.

kinetic Quartz nucleus = 100

kinetic Quartz nucleus = 100, CritSI = 0.1


The example above makes the nucleation area for quartz available only when the mineral has a saturation state ≥ 0.1. The default value for this option is 0, which means that the prescribed nucleation area is available whenever the mineral is supersaturated.

4.3 Forward and reverse reactions In React, you most commonly set a kinetic law describing the forward rate of a reaction. In this case, a positive r k→ indicates a mineral is dissolving, a complex dissociating, a gas dissolving into the fluid, or a redox or microbial reaction proceeding from left to right. You can alternatively specify that evaluating the rate law gives a positive result for the reverse reaction: precipitation, association, gas exsolution, or right-to-left progress.

The dissolution of quartz

SiO2(qtz) → SiO2(aq) (4.5)

for example, might be described by the rate law

r k→ = AS k+ �1− QK� (4.6)

where r k→ is dissolution rate, AS is surface area, k+ is the rate constant, and Q and K are the reaction’s activity product and equilibrium constant. Taking k+ at 70°C to be 2 × 10–16 mol/cm2 sec and AS as 103 cm2/g, you can set this rate law from the Reactants pane as shown below


or by typing

Selection of the “dissolution” option specifies that the law describes the dissolution (forward) reaction, which is the default behavior.

If we write the reverse reaction, for precipitation,

SiO2(qtz) ← SiO2(aq) (4.7)

the activity product Q⃖�� = 1/Q and the equilibrium constant K⃖�� = 1/K. Noting that K = k+/ k⃖�+ is the ratio of the rate constants for the forward and reverse reactions, and that Q = aSiO2 (aq), the rate law for this reaction is

r⃖k�⃗ = −rk�⃗ = AS k⃖�+ aSiO2 (aq)�1 − �⃖�𝑄�

�⃖�𝐾�� (4.8)

K at 70°C is 10–3:39, so k⃖�+ is 4.9 × 10–13.

kinetic Quartz forward rate_con = 2e-16 surf = 1000


The input below

or the command

sets this law, which is equivalent in function to the forward law described previously.

4.4 Kinetics of complexation and sorption React can trace the association and dissociation of any number of aqueous complexes, as well as surface complexes. The program uses a built-in rate law of the form

rk�⃗ = nw k+ � j

�aj | mj�𝑝𝑝j �1−

QK� (4.9)

to calculate the reaction rate r k→, in mol/s. Here, nw is kg of solvent water, k+ is the intrinsic rate constant (molal sec–1, in the absence of promoting and inhibiting species), pj are

kinetic Quartz reverse \ rate_con = 2e-12 surf = 1000 apower(SiO2(aq)) = 1


powers applied to the activities aj or molalities mj of the promoting and inhibiting species, and Q and K are the reaction’s ion activity product and equilibrium constant.

Reactions in React are written for species dissociation, so if you set a rate law for a forward reaction, r k→ is positive when the complex decomposes. The built-in law can assume the nonlinear form,

rk�⃗ = sgn �1 − QK� nw k+ �

j

�aj | mj�𝑝𝑝j �1 − �

QK�ω�Ω

(4.10)

in which ω and Ω are the nonlinearity coefficients, or reaction orders. When you set either nonlinearity coefficient to a value other than 1, the program uses the nonlinear law. You can, of course, set your own rate equation, rather than using the built-in law.

Set the initial concentration of a kinetic complex directly within its entry on the Reactants pane

or by typing

The input specifies a 200 𝜇𝜇molal concentration for the CaSO4 ion pair, at the beginning of the run. Note that the basis must be set to contain at least this much total calcium and sulfate, or the program will not be able to distribute mass. If you do not set an initial concentration, or set it to ?, the program will take the complex at the onset of the run to be in equilibrium with the initial fluid.

In X1t and X2t, click to expand the “fluid concentrations” box, then set the concentration of the kinetic complex in each boundary fluid:

kinetic CaSO4 200 umolal


Alternatively, type

As with the initial fluid, if you omit this setting, or specify an argument of ?, the complex will be set to its equilibrium concentration.

As an example, the complexation of aluminum and fluoride ions

AlF++ ← Al+++ + F– (4.11)

can be described by the rate law dmAlF++

dt =

r⃖k�⃗

nw = k⃖�+ mAl+++ mF– �1−

Q⃖��

K⃖�� (4.12)

Open the “Association.rea” input file and move to the Basis pane,

which defines the initial system, including the total amount of aluminum and fluoride dissolved in the water.

kinetic PbPO4- my_boundary = 0.3 umolal, my_injection = ?


On the Reactants pane, the kinetic rate law

causes the program to trace the complexation of alumina and fluoride over the course of a day, assuming a rate constant of 32.6 molal/s.

From the Command pane, type

Al+++ = 10 umolal F- = 10 umolal Cl- = 1 mmolal Na+ = 1 mmolal pH = 5 kinetic AlF++ 1 nmolal, reverse, rate_con = 32.6, \ mpower(Al+++) = 1, mpower(F-) = 1 suppress AlF2+, AlF3, AlF4-, AlF5-- precip off time end 1 day go


The calculation result shows the association of the AlF+ + ion pair, calculated according to a kinetic rate law.

Take as a second example the desorption of calcium

>(w)FeOCa+ + H+ → >(w)FeOH + Ca++ (4.13)

in a pH-buffered fluid, due to the decomposition of the >(w)FeOCa+ surface species. Assume the reaction is described by the rate equation

−dm>(w)FeOCa+

dt=

rk�⃗

nw= k+ m>(w)FeOCa+ �1 −

QK� (4.14)

Take a rate constant k+ of 2 × 10–4 molal/s, and the initial concentration of the surface complex to be 1500 𝜇𝜇molal.


Open “Desorption.rea” and go to the Basis pane,

where the initial fluid in equilibrium with a ferric hydroxide is set up. The simulation is set to span 12 hours.

Going to File → Open → Sorbing Surfaces…

to see that the Dzombak and Morel dataset for ion complexation with the hydrous ferric oxide is loaded.



Set a pH buffer and the rate law for calcium desorption. Take a rate constant k+ of 2 × 10–4 molal/s, and the initial concentration of the surface complex to be 1500 𝜇𝜇molal. The results are show here.


4.5 Gas transfer kinetics React can account for the kinetics of gas transfer between a fluid and an external gas reservoir, such as the atmosphere. The program calculates the rate rk�⃗ (mol/s) at which a kinetic gas Ak�⃗ dissolves into a fluid using the built-in equation rk�⃗ = nw Asp k+ �fext − fk�⃗ � (4.15)

Here, nw is solvent mass (kg), k+ is the rate constant (mol/cm2 sec), Asp is the specific contact area (cm2/kg solvent) between reservoir and fluid, and fext and fk�⃗ are the fugacities of 𝐴𝐴𝑘𝑘�⃗ in the external reservoir and the fluid. Where gas exsolves from the fluid, rk�⃗ is negative.

Parallel to the other kinetic features, you can specify promoting and inhibiting species, in which case, the law takes the form

rk�⃗ = nw Asp k+ ��aj| mj�𝑝𝑝j

j

�fext − fk�⃗ � (4.16)

You can set a nonlinear law

rk�⃗ = sgn�fext − fk�⃗ � nw Asp k+ ��aj| mj�𝑝𝑝j

j

�fext − fk�⃗ �Ω

(4.17)

in which Ω is the nonlinearity coefficient (there is no ω in the gas transfer model). And, as before, you can specify your own rate equation, instead of using the built-in law.

To set up kinetic gas transfer, you generally set the gas’ fugacity fext in the external reservoir, or its partial pressure Pext

, there; the model converts a pressure value to fugacity internally. You furthermore set the contact area between the fluid and external reservoir, in units of cm2/kg.

On the Reactants pane, at the top of the field for a gas transfer reaction, you constrain the external reservoir by entering a value and choosing either “fugacity” or a unit of pressure from the pulldown. Working from the command line, use the f_ext keyword to set external fugacity, and p_ext plus an optional unit to set partial pressure; the default unit is bar.

If you do not specify a value for external fugacity, the program takes it as the gas’ fugacity in the initial system, at the onset of reaction. Finally, you set the contact area on the next line in the Reactants pane, or with the contact keyword on the command line.


Having added a kinetic gas reaction, the Reactants pane might look like

Alternatively, we might type the command

These cases set up a kinetic reaction for the transfer of O2(g) between the fluid and an external reservoir in which 𝑓𝑓𝑂𝑂2 is 0.2. The contact area Asp in this case is 5 cm2/kg and the rate constant k+ is 3.4 × 10–7 mol/cm2 sec.

As a worked example, we trace the degassing of CO2 from a well-mixed surface water. Open “GasTransfer.rea” and go to the Basis pane

kinetic O2(g) f_ext = 0.2, contact = 5, rate_con = 3.4e-7


to see the fugacity in the water initially is 10–3. Move to the Reactants pane,

and set the details of the kinetic rate law. The fCO2 in the atmosphere is 10−3.5. The water is 125 cm deep, so Asp is 8 cm2/kg, and assume a rate constant k+ of 2 × 10−7. The results are shown here.

.


4.6 Kinetics of redox reactions You can use React to trace the progress over time of redox reactions, as described by kinetic rate laws. There is no limit to the number of kinetic redox reactions you can consider in a single simulation.

The kinetic rate law for a redox reaction is often presented in the form,

rk�⃗ = nw k+ ��aj|mj�

𝑝𝑝j

j

(4.18)

where nw is the mass of solvent water (kg), and k+ is the intrinsic rate constant (expressed in molal sec–1). The product function ∏ in this equation accounts for the reactant, promoting and inhibiting species j in the rate law; the activity or molality of each such species appears raised to its power pj. Each of these species may be an aqueous species, mineral, surface species (in which case it is represented by its molality), gas (by fugacity), or solvent (by activity).

If this equation is generalized to account for reverse as well as forward reaction, it takes the form,

rk�⃗ = nw k+ ��aj|mj�pj

j

�1− QK� (4.19)

where Q and K are the reaction’s activity product and equilibrium constant. This equation may in turn be generalized into a nonlinear form,

rk�⃗ = sgn �1 − QK� nw k+ ��aj|mj�

pj

j

�1 − �QK�𝜔𝜔�Ω

(4.20)

where ω and Ω are the nonlinearity coefficients (the rate law orders). This is the general form of the rate law that React carries for redox reactions.

To set up a kinetic redox reaction, begin by decoupling the redox couple in question, so that the reaction is not in equilibrium initially. Then set up the kinetic reaction and the form of the rate law.


As an example, go to the Config → Redox couples… dialog and decouple the Fe+ + +/Fe+ + pair,

then move to the Reactants pane and click → Kinetic → Redox reaction, supplying the info below.


Alternatively, type

Either way, these steps set a rate law dMFe+++

dt= nw k+ mFe++ mO2 (aq) aOH–2 �1−

QK� (4.21)

arbitrarily labeled “redox-1”, for the redox reaction, Fe++ + 1

4⁄ O2(aq) + 52⁄ H2O → Fe(OH)3 + 2 H+ (4.22)

where MFe+++ is the mass in the system of component Fe+ + + (mol), and k+ is the rate constant, 10–12 molal–1 sec–1. Notice that the redox reaction is set explicitly as a character string. The program parses the string to derive the coefficients and species in the reaction.

The following procedure models the oxidation of ferrous iron by molecular oxygen, assuming that the reaction produces ferric hydroxide, as might occur in a pH-buffered laboratory experiment left open to oxygen in the atmosphere.

Double-click the “Redox.rea” input file and go to the Config → Redox couples… dialog.

Here, the reaction between ferrous and ferric iron has been disabled. Iron in the simulation can therefore change redox state only by kinetic reaction.

decouple Fe+++ kinetic redox-1 \ rxn = "Fe++ + 1/4 O2(aq) + 5/2 H2O -> Fe(OH)3(ppd) + 2 H+" \ mpower(Fe++) = 1 mpower(O2(aq)) = 1 apower(OH-) = 2 \ rate_con = 1e-12


The Basis pane

shows the fluid’s initial composition. The ferrous and ferric components are constrained separately, since the Fe+ + +/Fe+ + redox pair is decoupled.



The “fix pH” and “fix fugacity of O2(g)” options simulate reaction in a pH-buffered laboratory experiment left open to oxygen in the atmosphere.

Click on the button next to reactant “redox-1” to expand its entry. The reaction by which the ferrous iron component oxidizes has been written out explicitly as a character string that the program will read and interpret. If the kinetic reaction hadn’t already been created, you would click on → Kinetic → Redox reaction to do so.


To keep the discussion simple for the moment, the iron minerals Goethite, Hematite, and Magnetite are suppressed, each of which is more stable and slower to form than ferric hydroxide precipitate.

Select Run → Go to calculate the model. The figure below shows the results of modeling the oxidation of ferrous iron by dioxygen, according to a kinetic rate law.

React can also account for the effects of heterogeneous catalysis, enzymes, and biological activity on the rates of redox reactions; these features are described in the following sections.


4.6.1 Catalysis on mineral surfaces React can account for the catalytic effects of mineral surfaces on redox reactions. The rate law in this case

rk�⃗ = AS k+ ��aj|mj�pj

j

�1− QK� (4.23)

is of the form of the previous equation, with the additional term AS, which represents the surface area (cm2) of the catalyst. The rate constant k+ here, in the absence of promoting and inhibiting species, is given in units of mol cm–2 sec–1. The rate law in nonlinear form is

rk�⃗ = sgn �1− QK� AS k+ ��aj|mj�

pj

j

�1 − �QK�𝜔𝜔�Ω

(4.24)

Again, this law is the same as the previous nonlinear form, with the additional term AS.

You set a catalytic redox reaction in the “catalyst” section of the rate law. Set the “catalyst” to the name of the mineral serving as a catalyst,

or simply to “on”.


Or, use the catalyst keyword in a kinetic command

Setting a value of “off” disables the feature.

Set the catalyzing surface area using the “catalytic area” field

or by typing

If you have set a specific mineral as the catalyst, its surface area is set in cm2/g; the program calculates total surface area from this value and the mineral mass, as it varies over the simulation. If you have simply set “catalyst” to “on”, on the other hand, the total catalyzing surface area is set in cm2.

Note that it is possible to set parallel pathways for the same redox reaction. Reaction “redox-1”, for example, could represent the reaction kinetics in the absence of a catalyst, and “redox-2”, the catalyzed reaction. The total reaction rate would be the sum of the rates for “redox-1” and “redox-2”.

The following procedure shows an example of how to incorporate redox catalysis into a React simulation. Here, the oxidation of Mn+ + to manganite (MnOOH) by molecular oxygen is catalyzed on the surface of ferric hydroxide.

kinetic redox-1 catalyst = Goethite kinetic redox-1 catalyst = on

kinetic redox-1 surface = 20


Double-click on file “Catalysis.rea” and go to the Config → Redox couples… dialog.

Note how we’ve disabled all redox coupling reactions. Alternatively, individual reactions can be decoupled: those between ferrous and ferric iron, as well as the reactions between several oxidation states of manganese. Either way, iron and manganese in the simulation can change redox state only by kinetic reaction.

Look at the Basis pane.

Consider a system containing reduced and oxidized manganese, as well as ferric hydroxide, which provides the catalyzing surface for manganese oxidation.


Move to the Reactants pane and expand the entry for reactant “redox-1”.

Fix the pH and O2(g) fugacity to simulate a buffered experiment. Expanding the entry for reactant “redox-1” allows you to view the details of the kinetic rate law specified.


On the Config → Suppress… dialog

note that various iron and manganese minerals have been suppressed because they are stable, but unlikely to form over the time span of the simulation.

Select Run → Go to calculate the model.

4.6.2 Enzymes and biotransformations React can trace the progress of enzymatically or biologically promoted redox reactions. In considering the effects of enzymes, the most commonly encountered rate law is the Michaelis-Menten equation. This equation may also be used in simple cases to model biotransformations (microbes are sometimes referred to as “bags of enzymes”).

To construct more sophisticated models of enzymatic and the microbe-mediated reactions, especially for cases in which microbial populations vary with time, see the section Microbial metabolism and growth, below.

The Michaelis-Menten equation represents the reaction of a substrate A with an enzyme E to form an activated complex EA, which decomposes irreversibly to give the reaction product P and return the enzyme:

A + E EA P + E (4.25)

The corresponding rate equation takes the well-known form,

rk�⃗ = nw k+ mE mA

mA + KA (4.26)


where k+ is the intrinsic rate constant (k+ = k3, in sec–1), mE is the molal concentration of the enzyme, mA is the substrate concentration, and KA is the half-saturation constant

KA = k2 + k3

k1 (4.27)

in molal units. The product k+ * mE is the maximum reaction rate (molal sec–1), commonly denoted rmax or vmax.

The reaction can be generalized by including the back reaction of products with enzyme to form the activated complex:

A + E EA P + E (4.28)

The rate law in this case takes the form,

rk�⃗ = nw k+ mE

mAKA

1 + mAKA

+ mPKP

�1− QK� (4.29)

where KP is the half-saturation constant

KP = k2 + k3

k4 (4.30)

for the reverse reaction, in molal, and mP is the molal concentration of reaction product P. Note that when P is at small concentration, Q becomes small also, and the rate law reduces to the Michaelis-Menten equation.

React carries a generalized rate law to model enzymatic reactions and biotransformations. The rate law in linear and nonlinear forms is given as

rk�⃗ = nw k+ ��aj|mj�pj

j

mE

mAKA

1 + mAKA

+ mPKP

�1− QK� (4.31)


and

rk�⃗ = sgn �1 − QK� nw k+ ��aj|mj�

pj

j

mE

mAKA

1 + mAKA

+ mPKP

�1 − �QK�𝜔𝜔�Ω

(4.32)

You set the reaction to be modeled using the rxn keyword, as before. It is important to

note that the program takes the first species on the left of the reaction to be the limiting substrate, and the first species on the right to be the limiting reaction product (i.e., the limiting substrate for the reverse reaction). The program tracks the concentrations of these species over the course of the simulation and uses them as the values for mA and mP.

For example, in the following input

the acetate is the limiting substrate, and methane is the limiting product. Throughout the simulation, the program will use mCH3COO- as mA, and mCH4(aq) as mP . If we were to reverse the order of the species on the right of the reaction, however, the program would take mHCO3- as mP. The way you write the redox reaction, therefore, affects the modeling results.


Set the identity of the enzyme using the pulldown next to “enzyme” (or use the mE keyword). You can select Aqueous… from the pulldown,

then choose an aqueous species in the simulation from the list. In this case, the program, over the course of the simulation, finds the molality of this species and uses it as mE.

Alternatively, select “on” from the pulldown to set the enzyme molality to a constant value, which you enter in the “mE” field.

By selecting “activity” instead of “molality” (or using keyword aE in place of mE), you can specify the activities rather than molalities of the enzyme and the limiting reactant and product species to be used to evaluate the rate law. In this case, the program replaces variables mE, mA, and mP in the rate law shown above with aE, aA, and aP .

Setting “enzyme” to “off” disables the feature.

You set the values for the half-saturation constants KA and KP in molal units using the “Ka” and “Kp” fields

(or the KA and KP keywords from the command pane), but you can omit a value for KP, in which case the program will not carry the mp/Kp term in the rate equation.


The following example models the biotransformation of acetate to bicarbonate by reaction with molecular oxygen, in an experiment open to atmospheric O2 and CO2. Double-click on file “Enzyme.rea” and go to the Config → Redox Couples… dialog.

Note how the reaction between acetate and inorganic carbon has been disabled. As a result, carbon in the simulation can change redox state only by kinetic reaction.

Look at the Basis pane,

which describes a fluid with acetate in equilibrium with O2 and CO2 in the atmosphere. The simulation is set to span 1 hour.


Move to the Reactants pane and expand the entry for reactant “redox-1”.

Fix the pH and O2(g) fugacity to simulate an experiment open to the atmosphere. Taking a value of 8 × 10–6 molal sec–1 for rmax, configure the simulation by setting “mE” to an arbitrary value of 1, and then k+ to the value of rmax, since rmax = k+ * mE, as described earlier.


Alternatively, type

Select Run → Go to calculate the model.

4.7 Microbial metabolism and growth React can trace the effect of microbial metabolism and growth in a geochemical system using a generalized kinetic rate law. As described below, the generalized rate law simplifies under specific conditions to each of the rate laws commonly used in microbial ecology.

In React, a microbe’s metabolism is assumed to be based on the transfer of electrons from a donating half reaction

� vDDD

⇆ � vD+

D+D+ + n e– (4.33)

to an accepting half reaction

� vA+A+

A+ + n e– ⇆ � vAA

A

(4.34)

Here, D and D+ represent species on the reduced and oxidized sides of the donating half reaction, A and A+ represent the same for the accepting half reaction, and n is the number of electrons transferred. The microbe’s overall metabolic reaction is the sum

time end = 1 hr decouple CH3COO- CH3COO- = 0.2 mmolal pH = 7 10 free mg/kg O2(aq); fix a O2(aq) swap CO2(g) for HCO3- log f CO2(g) = -3.5; fix f CO2(g) Na+ = 1 mmolal Cl- = 1 mmolal kinetic redox-1 rxn = "CH3COO- + 2 O2(aq) -> 2 HCO3- + H+" \ rate_con = 8e-6 mE = 1 KA = 5e-3


� vDDD

+ � vA+A+

A+ ⇆ � vD+

D+D+ + � vAA

A

(4.35)

of the half reactions.

4.7.1 Metabolic rate React calculates the metabolic rate (mol/s) for the progress of a microbial reaction according to the generalized rate law

rk�⃗ = nw k+[X]

(4.36) ×

�mjp

j

× TPF �KD �m

D+PD+

D+ + �mD

PD

D

�PKD

�KA �mAPA

A

+ �mA+PA+

A+�

PKA

where nw and [X] are, as before, water mass (kg) and biomass concentration (mg/kg), k+ is the rate constant (mol/mg s), mj and pj are the molaities and the powers in the numerator term of the promoting and inhibiting species (which generally appear in the metabolic reaction, although this is not a requirement), PD and PA, are the powers in the denominator term for various species in the metabolic reaction, KD and KA are the half-saturation constants for the donating and accepting reactions (varying units, in mol, kg, and s), and PKD and PKA are the overall powers of the KD and KA terms.

Variable TPF is the thermodynamic potential factor, given by

TPF = �1 − �

QK�𝜔𝜔

exp �−𝜔𝜔nATP∆𝐺𝐺ATP

RTK��

Ω (4.37)

where Q and K are the ion activity product and equilibrium constant for the metabolic reaction, and ω and Ω are the rate law orders, as before. Variable nATP is the number of moles of ATP produced per mole of progress of the metabolic reaction, ∆GATP is the free energy of ATP hydrolysis (the reaction by which adenosine tri-phosphate, ATP, decomposes to adenosine di-phosphate, ADP), R is the gas constant, and TK is absolute temperature.


The TPF is similar to the (1 − Q/K) terms in the other rate laws carried by React, except for the exponential term, which accounts for the fact that, to live, the microbe must derive enough energy from its environment to synthesize ATP, the cellular energy store, from ADP.

Note that in contrast to the other types of kinetic reactions, React assumes that a microbe’s metabolic reaction proceeds only in the forward direction. In other words, the program enforces rk�⃗ ≥ 0 for all cases.

To construct a microbial model, click → Kinetic → Microbial Reaction, set the metabolic reaction in the “reaction” field (or with the rxn or reaction keyword), as before, and specify a rate constant (keyword rate_con) and the reaction orders ω and Ω (order1 and order2). Set the half-saturation constants KD and KA for the donating and accepting reactions using the “Kd” and “Ka” fields (or with the KD and KA keywords); by default, these variables take a value of 0.

Set the powers pj, PD, and so on, of species molalities in the numerator of the rate equation by clicking under “power”

and selecting a species from the pulldown, or with the mpower (or mpow) keyword, as shown below.


For the terms in the denominator of the rate law, set the power PD and PD+ of species from the donating reaction by clicking under “powerD”, or using the mpowerD (or mpowD) keyword, and those from the accepting reaction (PA and PA+) by clicking under “powerA”, or with mpowerA (or mpowA). You can use the “activity” button or keywords apower, apowerD, or apowerA to set in the rate law a species’ activity in place of its molality, as shown below.

Use keywords PKD and PKA to set the exponents PKD and PKA for the grouped terms in the denominator. Keyword ATP_number sets the value of nATP, and ATP_energy sets ΔGATP, in kJ/mol.

You set the initial biomass of the microbial population in mg/kg, using the biomass keyword.

Over the simulation, React determines the rate of change in the biomass [X] from the calculated metabolic rate rk�⃗ according to the relation d[X]

dt =

Y rk�⃗

nw − D[X] (4.38)

where Y is the growth yield, and D is the decay constant. Specify these parameters in mg/mol and sec−1, respectively, using the growth_yield and decay_con keywords.


4.7.2 Relationship to other rate laws React’s microbial rate law reduces under specific conditions to each of the variety of empirical and semi-empirical rate laws commonly applied in microbial ecology. These rate laws include the following equations:

First-order dCdt

= k mD

Michaelis-Menten dCdt

= k mD

KD + mD

Zero-order dCdt

= k

Logistic dCdt

= k [X] mD

Monod dCdt

= k [X] mD

KD + mD

Dual-Monod dCdt

= k [X] mD

KD + mD

mA+

KA + mA+

Logarithmic dCdt

= k [X]

Here, C is the concentration of a product species (or the negative concentration of a substrate of electron accepting species), k is a rate constant in appropriate units, [X] is biomass concentration, mD and mA+ are activities of the limiting reactants in the donating and accepting half reactions, and KD and KA are the corresponding half-saturation constants. (The first-order, Michaelis-Menten, logistic, and Monod equations are commonly written in terms of a limiting species from the donating reaction, as shown, but may also be cast in terms of a species from the accepting reaction. In this case, mA+ replaces mD, and KA takes the place of KD in the equations above, as well as in Table 4.2).

To invoke one of these laws in React, set the appropriate parameters in your input, as shown in Table 4.2. In each case, set an appropriate value for the rate constant (keyword rate_con). You can set the rate law order Ω (“order2”) to 0,


which negates the thermodynamic potential function and hence casts the laws in the exact form shown above. Alternatively, you can leave Ω at its default value of 1, which will prevent the metabolic reaction in the simulation from proceeding beyond the point of equilibrium, which, of course, is a chemical impossibility.

Table 4.2 Settings for casting microbial rate law in terms of the various empirical equations. Symbol ✓ indicates an appropriate value should be set; x, no value is set. Symbols D and A+ represent names of limiting reactants in donating and accepting half reactions.

rate law mpow

(D)

mpowD

(D)

mpow

(A+ )

mpowA

(A+ )

KD

KA

biomass

growth_

yield

decay_

con

First-order 1 x x x x x 1 0 0

Michaelis-Menten

1 1 x x ✓ x 1 0 0

Zero-order x x x x x x 1 0 0

Logistic 1 x x x x x ✓ ✓ ✓

Monod 1 1 x x ✓ x ✓ ✓ ✓

Dual Monod 1 1 1 1 ✓ ✓ ✓ ✓ ✓

Logarithmic x x x x x x ✓ ✓ ✓

4.7.3 Example calculation As an example, we consider two microbial strains growing by oxidizing acetate (Ac) CH3COO− + 2 O2(aq) → HCO3

− + H+ (4.39)

in a chemostat experiment open to the atmosphere. The microbes’ metabolic rate is defined by

rk�⃗ = k+ [X] mAc

KD + mAc × TPF (4.40)

where the thermodynamic potential factor is


TPF = 1 − �

QK�

14⁄

exp�− 1

4 nATP ∆GATP�RTK

� (4.41)

One of the strains is faster at metabolizing than the other (it has a higher k+), whereas the second is more efficient (lower kD). Double-click on file “Microbes.rea” and go to the Config → Redox Couples… dialog.

Note how the reaction between acetate and inorganic carbon is disabled. As a result, carbon in the simulation can change redox state only by kinetic reaction.


Look at the Basis pane,

which describes the initial fluid composition in a chemostat experiment open to the atmosphere.



Fix the pH and gas fugacities to simulate an experiment open to the atmosphere. The simple reactants and the value set for “reactants times”, combined with the

“flush” option enabled from the Config → Stepping… dialog, cause the fluid in the chemostat to be replaced by a 20 μmolal Na-CH3COO solution 10 times.

Expand the entries for reactants “microbe-1” and “microbe-2” to view the details of the kinetic rate laws specified.

The first strain is faster at metabolizing than the second (it has a higher k+), whereas the second is more efficient (lower KD).


The following commands configure the same simulation.

decouple CH3COO- time end = 30 day Na+ = 50 mmolal Cl- = 50 mmolal CH3COO- = 1 umolal balance on Na+ pH = 7 fix pH swap O2(g) for O2(aq) f O2(g) = 0.2 fix O2(g) swap CO2(g) for HCO3- log f CO2(g) = -3.5 fix f CO2(g) kinetic microbe-1 \ rxn = "CH3COO- + 2 O2(aq) -> 2 HCO3- + H+", \ rate_con = 2e-6, KD = 2e-5, \ mpower(CH3COO-) = 1, mpowerD(CH3COO-) = 1, \ order1 = 0.25, ATP_energy = -48, ATP_number = 3, \ biomass = .001, growth_yield = 900, decay_con = 8.33e-6 kinetic microbe-2 \ rxn = "CH3COO- + 2 O2(aq) -> 2 HCO3- + H+", \ rate_con = .6e-6, KD = 1e-5, \ mpower(CH3COO-) = 1, mpowerD(CH3COO-) = 1, \ order1 = 0.25, ATP_energy = -48, ATP_number = 3, \ biomass = .001, growth_yield = 450, decay_con = 1.67e-6 react 1 kg of H2O react 20 umol of CH3COOreact 20 umol of Na+ reactants times 10 flush


Select Run → Go to calculate the model. In the calculation results, the rapidly metabolizing strain grows fastest initially, but with time is replaced by the more efficient strain.

4.8 Chaining together kinetic paths You can use the pickup command (see Picking up the results of a run in the previous chapter) to chain together kinetic reaction paths. When you pick up the results of a calculation, React retains all or some of the kinetic reactions being traced, at their endpoint states. You can then initiate a subsequent simulation that traces continued progress of the kinetic reactions.

In the simplest case, when you pick up the entire system using Run → Pickup → System → Entire (or the command pickup),


the program retains whatever kinetic reactions are set. Using Run → Pickup → System → Fluid (or pickup fluid),

causes React to retain the kinetic reactions occurring within the aqueous phase—the kinetic redox and aqueous complexation reactions—for the new reaction path; kinetic reactions involving minerals, surfaces, a gas phase, or microbes are discarded.

Picking up the entire endpoint system, or just the endpoint minerals, as reactants (i.e., pickup reactants or pickup reactants = minerals) causes the program to retain the kinetic reactions involving mineral precipitation and dissolution. The pickup reactants = minerals command, then, lets you model experiments in water-rock interactions in which minerals react kinetically with a fluid that is periodically refreshed.

To see how kinetic reactions can be chained together, start by simulating the kinetic dissolution of quartz in dilute water at 100°C:

We wish to figure the effect, after reacting the quartz for 10 hours, of adding a reaction promoter to the solution. To do so, pick up the calculation results, increase the rate constant by a factor of 5 to reflect the promoter, and run a second path.

time end = 10 hours T = 100 C SiO2(aq) = 1 umol/kg react 5000 g Quartz kinetic Quartz rate_con = 2.e-15 surface = 1000 go

pickup kinetic Quartz rate_con = 10.e-15 go


Over the course of the second reaction path, which begins at t = 10 hours and continues to t = 20 hours, quartz dissolves more rapidly than in the first, reflecting the increased value of the rate constant.

115

Custom Rate Laws

React’s built-in rate laws for mineral dissolution and precipitation, aqueous and surface complex dissociation and association, redox, microbe-mediated reactions, and gas transfer can be applied to the great majority of kinetic problems in geochemistry. For cases in which you wish to apply a rate law of a differing form, however, you can easily define one of your own.

You can define a rate law in any of three ways: 1. Specify its form as a character string. For example, you might set rate_con *

surface * (1 – Q/K) as a rate law. 2. Prepare a file that contains a script of commands for calculating the reaction

rate. Write the script in a simplified version of the MS Visual BASIC language, as described below.

3. Write and compile your own function for evaluating the rate law (you will probably want to use C++), and link it into a library. React, as it runs, opens the library and executes the function directly whenever it needs to evaluate the rate law.

Each method is described below.

5.1 Setting the rate law form directly The simplest method for defining a rate law is to specify its form as a character string. React contains an interpreter (prepared with the “Bison” compiler; see Further Reading) that converts the character string into computer instructions that React executes.

You set the form of the rate law with the rate_law parameter of the kinetic command. For example, you might enter the command

kinetic Quartz rate_law = "rate_con * surface * (1 – Q/K)", \ rate_con = 1e-18, surface = 1000


This command will cause the reaction rate for quartz to be calculated as the product of the rate constant, the mineral’s surface area, and its saturation.

Table 5.1 lists the parameters, such as rate_con, that you can use to set rate laws in this manner. There are also a number of “helper functions” that you can invoke; these are listed in Table 5.2. For example, in your script you can use the helper function activity("H+") to denote activity of the hydrogen ion.

In addition to these parameters, a number of parameters identifying the current nodal block and describing its properties are available in X1t and X2t. For a list of these parameters, see the appendix on Heterogeneity in the GWB Reactive Transport Modeling Guide.

If you enclose helper function arguments in double quotes ("), you need to delimit the rate law itself with single quotes ('). For example,

Alternatively, use single quotes to set off helper function arguments and double quotes for the rate law string.

5.2 Rate law scripts You can define more sophisticated rate laws by preparing a script in a simplified form of the BASIC language, as described in Table 5.3. Save the script in a file, the name of which must end with the extension .bas. You then specify the file’s name in the kinetic command with the rate_law parameter. For example, the command

tells React that the rate law for the reaction of Quartz is to be found in the specified file. You also use the kinetic command in the usual way to set any parameters used by your script, such as the rate constant or specific surface area, as shown above. React looks for your .bas file first in the current working directory, and then in the directory where the GWB is installed (for example, C:\Program Files\GWB). You can, of course, specify a full path name to the file, to avoid ambiguity.

Alternatively, you can set your rate law script directly within your input file. For example, the input

kinetic redox-1 rate_law = 'Wmass * molality("Na") * rate_con'

kinetic Quartz rate_law = My_script.bas rate_constant = 10^-16

kinetic Quartz rate_law = { rate = Wmass * rate_con / activity("H+") RETURN rate }

Custom Rate Laws 117

sets the rate law script directly, without need to refer to an external file. Your script can access the parameters in Table 5.1, as well as the “helper functions” in

Table 5.2. Parameters in rate law scripts are copies of the values carried internally by React; with four exceptions, these values cannot be changed from your script. The exceptions are the biomass, the two kinetic factors in the microbial model, and the thermodynamic potential factor (parameters “biomass”, “FD”, “FA”, and “TPF”), which you can set with the special function setgwbvar. For example, the entry

sets the current value carried by React for “biomass” to the value of “newbiom”, previously calculated in the script.

An example of a rate law script (the example scripts in this section are found in files within the “src” subdirectory, where the GWB is installed) is

In this example, the dissolution rate of a mineral is calculated from its rate constant, surface area, and saturation. The mineral’s rate of precipitation, should it appear supersaturated, however, is 0.

As a second example, we account in the rate law script for the effects of promoting and inhibiting species on a mineral’s reaction rate.

setgwbvar("biomass", newbiom)

IF QoverK < 1 THEN 20 ELSE 40 20: rate = rate_con * surface * (1 - Q/K) GOTO 60 40: rate = 0.0 60: RETURN rate

cat = 1.0 i = 1 begin_loop: IF i > ncatal THEN GOTO end_loop cat = cat * acatal(i)^pcatal(i) i = i + 1 GOTO begin_loop end_loop: rate = cat * rate_con * surface * (1.0 - QoverK) RETURN rate


Similarly, we could write a script to return the rate of a redox reaction in the form

As a final example, we construct a script to return the rate of microbial metabolism, taking Ω to be unity. In this case, we need to calculate how the microbial biomass and the thermodynamic potential factor vary, and update each in React’s memory space using the setgwbvar function, as described above.

cat = 1.0 i = 1 begin_loop: IF i > ncatal THEN GOTO end_loop cat = cat * acatal(i)^pcatal(i) i = i + 1 GOTO begin_loop end_loop: rate = Wmass * cat * rate_con * (1.0 - QoverK) RETURN rate

aff = QoverK * exp(-ATP_number * ATP_energy / (8.3143 * TK)) aff = aff^order1 IF (aff > 1.0) THEN aff=1.0 prod = 1.0 i=1 begin_loop1: IF i>ncatal THEN GOTO end_loop1 prod = prod * acatal(i)^pcatal(i) i=i+1 GOTO begin_loop1 end_loop1: prodKd1 = KD prodKd2 = 1.0 i=1 begin_loop2: IF i>nspecD THEN GOTO end_loop2 IF signD(i) > 0 THEN prodKd1 = prodKd1*actD(i)^powerD(i) IF signD(i) < 0 THEN prodKd2 = prodKd2*actD(i)^powerD(i) i=i+1 GOTO begin_loop2 end_loop2:


Note the technique used in this script to update the biomass. The time rate of change in biomass concentration is given as

d[X]dt

= Yrk�⃗

nw− D[X] (5.1)

as described in the previous section of this guide. We can re-express this relation in integral form to give biomass concentration [X] at the end of a reaction step

(cont’d) prodKa1 = KA prodKa2 = 1.0 i=1 begin_loop3: IF i>nspecA THEN GOTO end_loop3 IF signA(i) > 0 THEN prodKa1 = prodKa1*actA(i)^powerA(i) IF signA(i) < 0 THEN prodKa2 = prodKa2*actA(i)^powerA(i) i=i+1 GOTO begin_loop3 end_loop3: tpf = 1.0 - aff fd = prodKd2 / (prodKd1 + prodKd2)^PKD fa = prodKa2 / (prodKa1 + prodKa2)^PKA setgwbvar("TPF", tpf) setgwbvar("FD", fd) setgwbvar("FA", fa) denom = (prodKd1 + prodKd2)^PKD * (prodKa1 + prodKa2)^PKA rprime = rate_con * (prod/denom) * tpf IF (Deltat <= 0.0) THEN GOTO end_block rprime0 = dndt0/(biomass0 * Wmass) rpave = (1.0-Theta)*rprime0 + Theta*rprime biom = biomass0*exp((growth_yield*rpave-decay_con)*Deltat) IF biom < 0.0 THEN biom = 0.0 setgwbvar("biomass", biom) end_block: return rprime * biomass * Wmass


[X] = [X]0 e�Y r′−D�∆t (5.2)

from the concentration [X]0 at the beginning of the step, the reaction rate r′ per unit biomass concentration per kg water (where rk�⃗ = r′nw[X]), and the step length ∆t.

5.3 Compiled rate laws If you have a little interest in programming, you may wish to write your own rate law function, most likely in C++. React, as it runs, can link to your function and call it directly. This method provides the most efficient and powerful way to define a custom rate law.

There are three steps in the procedure: 1. Write a function that returns the reaction rate (and optionally its derivatives) for

a kinetic reactant, using the “gwb_context.h” and “ratelaw_param.h” header files supplied with the GWB software release. Copies of these files are found in the “src” subdirectory, where the GWB is installed.

2. Compile the function and link it into a dynamic link library (or DLL). The DLL must end in the extension .dll. You may link, within a single library, one or several rate law functions.

3. In the React input, specify the names of the library and function, separated by a colon (:). For example, setting

Each rate law function takes three parameters: 1. An integer value i. When i is –1, the function should calculate reaction rate,

returning a value in mol/sec. When i is the index of a basis entry (i.e., it is in the range 0 to the number of basis entries, less 1), the function should calculate the derivative of reaction rate with respect to the indicated basis entry. Alternatively, the function may return the special value “ANULL”, in which case React will calculate the derivative itself, using finite differences.

2. Reference to a “Reactant” data structure that describes the kinetic reaction in question. This reference should be named “r”. The form of this data structure is defined in a header file “gwb_context.h”, which is distributed with the GWB.

3. Reference to a “GWBcontext” data structure that contains information about current conditions (temperature, ionic strength, and so on) in the React simulation. This reference is named “c”. Again, the form of this data structure is defined in “gwb_context.h”.

kinetic Quartz rate_law = my_lib.dll:my_ratelaw


The parameters in Table 5.1 are available to your function. These parameters are defined in a second header file “ratelaw_param.h”, which should be included at the top of the function. You can also use as parameters any of the entries in the “GWBcontext” data structure, as set out in “gwb_context.h”. In addition, the “helper functions” listed in Table 5.2 are available. To debug functions, use the printf function (but not cout) to display data.

As an example of a rate law function, consider a mineral that dissolves according to its rate constant, surface area, and saturation, but does not precipitate. Such a function, here named “example1”, can be written

Note the need to export the function from the DLL. We specify a C rather than C++ function, to avoid “name globbing” conflicts among compilers. Also note that by returning “ANULL” when React requests a derivative, we tell React to compute these values itself, using finite differences.

To compile the DLL, open your compiler’s 64-bit command line environment corresponding if you have 64-bit GWB version installed on your computer, or the 32-bit environment if you are running 32-bit GWB. The commands

compile and link this function using the Microsoft C++ compiler, and

#define EXPORT extern "C" __declspec(dllexport) #include <windows.h> #include <stdio.h> #include <math.h> #include "gwb_context.h" EXPORT double example1(int i, Reactant &r, GWBcontext &c) { #include "ratelaw_param.h" if (QoverK > 1.0) // Mineral does not precipitate. return 0.0; else if (-1 == i) // Dissolution rate. return rate_con * surface * (1.0 - QoverK); else // Let React determine derivatives. return ANULL; }

cl /MD /O2 /c example1.cpp link /dll example1.obj react.lib /out:mylib.dll


do the same for the Intel C++ compiler. Here, file “example1.cpp” contains the C++ source, and “react.lib” is a short dataset supplied with the GWB; parallel files “x1t.lib” and “x2t.lib” are supplied for use with programs X1t and X2t.

Note you should change to a working directory in your file space before compiling and linking; the process will not work correctly in a system directory, such as \Program Files.

It is important to note that the internal data structures in the GWB will likely change as the software continues to evolve. You should preserve the source code for your rate law functions, so that you can recompile it for future software releases.

As a second example, we consider the same rate law, but instead of allowing React to compute the derivatives by finite differences, which can be time consuming, we calculate them directly. The forms of the derivatives are given in the Geochemical and Biogeochemical Reaction Modeling text (see Further Reading). The code (omitting the global headers) is:

icl /MD /O2 /c example1.cpp xilink /dll example1.obj react.lib /out:mylib.dll

EXPORT double example2(int i, Reactant &r, GWBcontext &c) { #include "ratelaw_param.h" if (QoverK > 1.0) return 0.0; else if (-1 == i) return rate_con * surface * (1.0 - QoverK); else if (H2O == i) // Derivative wrt water mass = zero. return 0.0; else if (i > H2O && i < c.Nbasis) // Other derivatives. return -rate_con * surface * mtcoef[i] * QoverK / Bas[i].c; else return 0.0; }


As a third example, we code a rate law that includes promoting and inhibiting species.

We consider in a fourth example how we might represent the rate law for a redox reaction.

In a final example, we write a function to calculate the rate of microbial metabolism, taking Ω to be unity. Note that, in this case, if we are to account for growth, we must update the microbial biomass (variable biomass); we also calculate the kinetic factors “FD” and “FA”, as well as the thermodynamic potential factor “TPF”, so they will be available in the program output.

EXPORT double example3(int i, Reactant &r, GWBcontext &c) { #include "ratelaw_param.h" if (-1 == i) { double cat = 1.0; for (int j=0; j<ncatal; j++) cat *= pow(acatal[j], pcatal[j]); return cat * rate_con * surface * (1.0 - QoverK); } else return ANULL; }

EXPORT double example4(int i, Reactant &r, GWBcontext &c) { #include "ratelaw_param.h" if (-1 == i) { double cat = 1.0; for (int j=0; j<ncatal; j++) cat *= pow(acatal[j], pcatal[j]); return Wmass * cat * rate_con * (1.0 - QoverK); } else return ANULL; }


EXPORT double example5(int i, Reactant &r, GWBcontext &c) { #include "ratelaw_param.h" double aff, rpave, rprime, rprime0; double prod, prodKd1, prodKd2, prodKa1, prodKa2; if (-1 == i) { aff = QoverK * exp(-ATP_number*ATP_energy/ (8.3143*TK)); aff = pow(aff, order1); aff = min(aff, 1.0); prod = 1.0; for (int j=0; j<ncatal; j++) prod *= pow(acatal[j], pcatal[j]); prodKd1 = KD; prodKd2 = 1.0; for (int j=0; j<nspecD; j++) if (signD[j] > 0) prodKd1 *= pow(actD[j], powerD[j]); else if (signD[j] < 0) prodKd2 *= pow(actD[j], powerD[j]); prodKa1 = KA; prodKa2 = 1.0; for (int j=0; j<nspecA; j++) if (signA[j] > 0) prodKa1 *= pow(actA[j], powerA[j]); else if (signA[j] < 0) prodKa2 *= pow(actA[j], powerA[j]); TPF = 1.0 - aff; FD = nspecD > 0 ? prodKd2 / pow(prodKd1 + prodKd2, PKD) : ANULL; FA = nspecA > 0 ? prodKa2 / pow(prodKa1 + prodKa2, PKA) : ANULL; rprime = rate_con * (prod / (pow(prodKd1 + prodKd2, PKD) * pow(prodKa1 + prodKa2, PKA))) * TPF; if (Deltat > 0.0) { rprime0 = dndt0 / (biomass0 * Wmass); rpave = (1.0 - Theta) * rprime0 + Theta * rprime; biomass = biomass0 * exp((growth_yield * rpave - decay_con) * Deltat); biomass = max(biomass, 0.0); }


The technique for updating biomass here is described in the previous topic, Rate law scripts.

Table 5.1 Internal parameters for defining rate laws. Parameters are case

sensitive.

Parameter Meaning

Chemical conditions

pH logfO2 Eh pe TDS IS SIS chlorinity Watact soln_density soln_viscosity alkalinity EC hardness hardness_carb hardness_ncarb

pH Log di-oxygen fugacity Redox potential (V) pe Dissolved solids (mg/kg) Ionic strength (molal) Stoichiometric Ionic strength (molal) Chlorinity (molal) Water activity Solution density (g/cm3) Solution viscosity (cp) Water alkalinity (mg/kg as CaCO3) Electrical conductivity (uS/cm) Total hardness (mg/kg as CaCO3) Carbonate hardness (mg/kg as CaCO3) Non-carbonate hardness (mg/kg as CaCO3)

Phases

Wmass soln_mass rock_mass soln_volume

Mass of solvent water (kg) Mass of fluid in nodal block (kg) Mass of minerals in nodal block (kg) Volume of fluid in nodal block (cm3)

(cont’d) return rprime * biomass * Wmass; } else return ANULL; }


rock_volume Volume of minerals in nodal block (cm3)

Reactant properties

name rxn, reaction mw mv order1 order2 ncatal catal (1), catal (2), … pcatal (1), pcatal (2), … xaffin catalyst enzyme KA KD KP nspecD specD(1), specD(2), … powerD(1), powerD(2), … signD(1), signD(2), … nspecA specA(1), specA(2), … powerA(1), powerA(2), … signA(1), signA(2), …

Reactant name Kinetic reaction, as a character string Mole weight of a kinetic mineral (g/mol) Mole volume of a kinetic mineral (cm3/mol) Rate law order ω for Q/K term Rate law order Ω for (1 – Q/K) term Number of promoting and inhibiting species in rate law Names of promoting and inhibiting species Powers (exponents) of promoting and inhibiting species Name of cross-affinity mineral Name of catalyst Name of enzyme Half saturation constant KA for forward reaction in enzyme model, and electron accepting reaction in microbial model Half saturation constant KD for electron donating reaction in microbial model Half saturation constant KP for reverse reaction, enzyme model Number of species in “KD” product functions in the microbial model Names of species in “KD” products Powers (exponents) of species in “KD” products Signs (+ for right side of reaction, - for left) of reaction coefficients for species in “KD” products Number of species in “KA” product functions in the microbial model Names of species in “KA” products Powers (exponents) of species in “KA” products Signs (+ for right side of reaction, - for left) of reaction coefficients for species in “KA” products


PKA PKD growth_yield decay_con ATP_energy ATP_number

Power (exponent) for KA term in microbial model Power (exponent) for KD term in microbial model Growth yield, microbial model Decay constant (/sec), microbial model Free energy of ATP synthesis (J/mol), microbial model Number of protons translocated in microbial model

Reactant status at nodal block

QoverK logQoverK Q K logQ logK moles, mass dndt dndt0 rate_con act_en pre_exp sparea surface nucleus critSI acatal(1), acatal(2), … a_enzyme actD(1), actD(2), … actA(1), actA(2), …

Q/K log Q/K Activity product Q for reaction Equilibrium constant K log Q log K Mass of a kinetic mineral (mol) Reaction rate (mol/sec) averaged over time step Instantaneous reaction rate (mol/sec) at beginning of time step Rate constant (in absence of promoting or inhibiting species: mol/cm2 sec, molal/sec, or molal/cm2 sec) Reaction activation energy (J/mol) Reaction pre-exponential factor (same units as rate constant) Specific surface area of a kinetic mineral Total surface area of a kinetic or catalyst mineral (cm2) Nucleation area of a kinetic mineral (cm2/cm3 fluid) Critical saturation index for nucleation Activities, molalities, fugacities of promoting and inhibiting species Enzyme molality or activity Activities, molalities, fugacities of species in “KD” products Activities, molalities, fugacities of species in “KA”


biomass biomass0 TPF FD FA mtcoef

products Biomass (mg/kg) at end of time step Biomass (mg/kg) at beginning of step Thermodynamic potential factor, microbial model Kinetic factor for donating reaction, microbial model Kinetic factor for accepting reaction, microbial model Mass transfer coefficient

Temperature

temperature, TC, Tempc TK

Temperature (°C) Temperature (K)

Domain

Nnode Nx Ny Length Width Height Radius1 Radius2 Wedge_angle

Number of nodal blocks in total Number of nodal blocks along the x direction Number of nodal blocks along the y direction Size of domain along the x direction (cm) Size of domain along the y direction (cm) Size of domain along the z direction (cm) Beginning radius of radial or spherical domain (cm) Ending radius of radial or spherical domain (cm) Radial angle of radial or spherical domain (radians)

Indexing

Inode Ix, Xindex Jy, Yindex

Node index Index of nodal block along the x direction Index of nodal block along the y direction

Nodal block

Xposition Yposition Deltax Deltay

Position of center of nodal block along the x direction (cm) Position of center of nodal block along the y direction (cm) Length of nodal block (cm) Width of nodal block (cm)


Deltaz bulk_volume, Vbulk inert_volume, Vinert Xfree freeflowing, Vfree stagnant, Vstag Xarea Yarea Poros0 porosity

Height of nodal block (cm) Bulk volume of nodal block (cm3) Non-reacting volume in nodal block (cm3) Free-flowing fraction of nodal block Volume of free-flowing zone in block (cm3) Volume of stagnant zone in block (cm3) Area (cm2) of nodal block normal to x direction Area (cm2) of nodal block normal to y direction Sediment initial porosity, as a fraction Sediment porosity, as a fraction

Time marching

Time Tstart Tend Deltat Theta Xi PV

Time (s) Starting time (s) Ending time (s) Length of time step (s) Time weighting variable Reaction progress Pore volumes displaced


Table 5.2 “Helper functions” available in rate law scripts. Each function takes a character variable or string as an argument and returns a numeric value. Function names are case sensitive.

“Helper function” Returns activity(species) Activity of a species (or fugacity of a gas) fugacity(gas) Fugacity of a gas gamma(species) Activity coefficient of a species boltzman(surface species) Boltzman factor for a surface species molality(species) Molal concentration of a free species gas_pressure(gas) Partial pressure of a gas (bar) mass(species) Mass of a species, mineral, or reactant (mol) totmolal(basis entry) Molal concentration of a component (a basis

entry, before swapping) in the fluid totmoles(basis entry) Moles of a component in the fluid totmoles_rck(basis entry) Moles of a component in the rock (minerals) totmoles_sys(basis entry) Moles of a component in the system totmoles_sor(basis entry) Moles of a component in the sorbate totmoles_col(basis entry) Moles of a component in mobile colloids totmoles_stg(basis entry) Moles of a component in the stagnant zone QovK(reactant) Q/K for a mineral or kinetic reaction logQovK(reactant) Affinity of a mineral or kinetic reaction surf_charge(surface type) Charge on a sorbing surface (C/m2) surf_potential(surface_type) Electrical potential of a sorbing surface (V) sorb_area(surface_type) Area of a sorbing surface (m2) Eh(redox couple) Redox potential of a redox couple (V) mw(species) Mole weight of a species or reactant (g/mol) mv(species) Mole volume, mineral or reactant (cm3/mol) species_index(species) Index in program arrays of aqueous species surf_index(species) Index of a surface species mineral_index(species) Index of a mineral species gas_index(species) Index of a gas species reactant_index(reactant) Index of a reactant surftype_index(surface type) Index of a surface type couple_index (couple) Index of a redox couple


Table 5.3 Summary of syntax for rate law scripts. Keywords are not case

sensitive.

LET variable = expression Assignment of a numerical value or character string. The LET is optional. Variable names start with a letter and may contain digits and underscore characters

label: statement Statement label, may be numeric or a character string

statement : statement A colon (:) separates statements on a single line

GOTO label Begin executing statements following label. GOTO and GO_TO are synonymous. The label may be a number or a character string Examples: GOTO 100 GOTO Line1

IF condition THEN statement or label ELSE

statement or label

Conditional execution; the ELSE clause is optional. The condition is false if it evaluates to 0, otherwise true. Example (appears on one line): IF x > 0 THEN 20 ELSE PRINT “too small”

REM comment A remark. Any characters until the end of the line are ignored.

+, -, *, /, ^, MOD Arithmetic operations, including exponentiation. Example: x + y

- Negation: - y =, <, >, <=, >=, <> Comparisons of numeric or character values,

such as x < y Comparison of character strings is case-insensitive

AND, OR, XOR, NOT Logical operators. Each except NOT takes two operands, such as x AND y

PI Value of 𝜋𝜋 (3.14159…)


(expression) Grouping and association: x * ( y + z )

ABS, EXP, LOG, LOG10, SQRT, SGN

Absolute value, exponentiation, natural and common logarithms, square root, and sign functions. EXP (x) is ex

SIN, COS, TAN, ASIN, ACOS, ATAN, SINH, COSH, TANH

Trigonometric functions (taking values in radians), their inverses, and hyperbolic trig functions

MIN, MAX Minimum or maximum of two values

DIM var1 (dimension), var2 (dimension)

Declare and allocate memory for one or more arrays. In the example: DIM A (3)

Array A has entries A (1), A (2), and A (3). Arrays may contain up to 1000 entries.

PRINT item1, item2 Print the numerical values or character strings in a list of items. Items are separated by commas, or by semicolons, in which case the corresponding values appear without an intervening space. Example: PRINT “rate_constant =”, rate_con

PAUSE item1, item2 Print any items listed and pause execution until the user touches a key. Syntax is the same as for the PRINT command

RETURN expression Terminate the program and return the value of “expression”

END Terminates the script. This statement is not required.

133

Using Gtplot

Gtplot is an interactive, mouse-driven program that produces various types of diagrams showing the results of tracing reaction paths with React.

After tracing a reaction path with React, start Gtplot by clicking on Plot Results on the Results pane, or selecting Run → Gtplot from React’s menubar. The program will read the calculation results from the “.gtp” file React produced and render them graphically. You can leave Gtplot active when you run further React simulations. Each time React completes a run, it signals Gtplot, which updates its display to reflect the new results.

You can also start Gtplot by opening any “.gtp” or “.gtc” file, or by clicking on the Gtplot icon on the Apps pane of the GWB dashboard. You can take input from a different dataset by choosing File → Open → Data File… from the menubar.

6.1 Initial plot Gtplot opens a window on your workstation screen, reads input data from a “.gtp” file, and renders the data as a two-dimensional plot. The window has three parts: a graphics area, a menubar with pulldown menus, and a frame showing the name of the input dataset and its activity model.


The initial plot shows how the mass of the various minerals in the React calculation varied with reaction progress ξ. The program, however, can make different kinds of plots that show the following types of variables:

Mass and volume of minerals in the modeled system Concentration, activity, and activity coefficients of dissolved species Elemental composition of the fluid, minerals, sorbate, and the bulk system Composition of the fluid, minerals, sorbate, and the bulk system, expressed in

terms of thermodynamic components Gas fugacity and partial pressure Saturation indices Q/K with respect to various minerals Bulk stable isotopic composition of the fluid, minerals, sorbate, and the entire

system, as well as the composition of individual species, gases, and minerals Fraction of various components sorbed onto mineral surfaces Variables such as temperature, pH, and reacted mass

In addition, you can plot the results of the React calculation on any of the special plot types, such as Piper and Durov diagrams (see Using Gtplot in the GWB Essentials Guide). Use the Plot menu to control the type of plot produced and the configuration of the plot.

Gtplot works using information about the system modeled, including its bulk composition (i.e., its composition in terms of Na+, Ca+ +, and so on), and the fluid’s pH, TDS, carbonate speciation, and so on. Some of the “special” plots show variables labeled “HCO3 + CO3”. Such plots show the sum of the concentrations in solution, in terms of electrical equivalents per kg fluid, of the free HCO3

– and CO3– species. The program

calculates this sum from the fluid’s carbonate alkalinity, as determined by the React

Using Gtplot 135

program. Hence, the value shown for the variable depends not only on carbonate concentration, but the fluid’s pH. In contrast, plots labeled “HCO3” represent the bulk carbonate concentration of the fluid, taking no account of the speciation of carbonate to the CO3

– , HCO3– , and CO2(aq) species.

When Gtplot starts for the first time in a given directory, it assumes a default configuration. Upon finishing, the program saves for its next run a dataset containing the current configuration of the plots. You can select options from the File menu to specify an alternative configuration (see Loading and saving plot configuration) or reset the entire program configuration.

6.2 XY Plot configuration Choose Plot → XY Plot… to specify the configuration of the xy plot. Alternatively, you can alter the configuration by interacting with the graphical aspects of the plot, such as any data line, data label, axis, tick mark, label, or grid line. A right-click on an aspect of the plot displays a menu showing the options available. Double-click on an aspect to invoke the XY Plot Configuration dialog. Dragging an inner or outermost axis tick mark, number, or grid line will shift or scale, respectively, the axis range, (see Using Gtplot in the GWB Essentials Guide).

The X Axis and Y Axis tabs let you select one variable to plot on the x axis, and one or more variables to plot on the y axis. Use Variable type to control the type of variables to appear along the plot’s axes. Variable type options are: Chemical parameters such as temperature, pH, and mass solution Physical parameters such as fluid density, porosity, and fluid velocity Reactant properties such as net reaction progress and reaction rates Components in the fluid, minerals, sorbate, and the bulk system (fluid plus

sorbate and rock) Component Kd’s of the various components that may be sorbed onto mineral

surfaces Sorbed Fractions of the various components that may be sorbed onto mineral

surfaces Species to plot either the concentration, activity, or activity coefficient of one or

more aqueous species Minerals to represent the masses or volumes of minerals over the reaction path Mineral Saturation to plot the saturation indices (Q/K) of the fluid with respect to

one or more minerals Gas partial pressure and Gas fugacity of one or more gases in the fluid Elemental Composition of the fluid, the rock, the sorbate (i.e., surface

complexes), or the system (fluid plus sorbate and rock)


Isotopic composition of the bulk fluid, rock, sorbate, and system, as well as individual species, for active isotope systems

Use the Filter menu to set, for species or mineral saturation plots, a basis species to consider. In a typical reaction path calculation, so many dissolved species are considered, and saturation states are determined for so many minerals, that the data fit poorly on a single plot. For this reason, Gtplot can group species and minerals into sets of just those that contain a given basis species. You can choose to plot, for example, the species containing Na+, or the saturation indices of minerals containing Al+ + +. Alternatively, you may choose to consider all species and minerals.

The selection of a variable type displays a list of possible variables. Click on a variable you wish to select. Use Ctrl+click to select multiple variables. Use Shift+click to select a range of variables.

Use the following to specify the way the variables are plotted: Variable type to control the type of variables to appear along the plot’s axis. Consider to list, for species or mineral saturation plots, the set of just those that

contain a given basis species. Auto-scale to set the data range for the axis to span the data to be plotted. Minimum, Maximum, and Tick increment to set the data range for the axis. Reverse axis to reverse the sense of the axis. Units to select alternative units, if any, for the axis. As to plot values as elemental equivalents, or as protonated or deprotonated

species equivalents. Type to set the axis to a linear, log, or delta scale. A delta scale shows change in

a variable’s value from the initial point in the reaction path. First, Previous, Next, and Last to cycle through the variable choices.

Using Gtplot 137

6.3 Plot types In addition to using the xy plot, you can plot the results of the React calculation on any of the special plot types, including as a ternary diagram, Piper diagram, Durov diagram, Schoeller diagram, Stiff diagram, radial plot, bar chart, and pie chart. Use the Plot menu to control the type of plot produced and the configuration of the plot. Each selection invokes a dialog box specific to the type of plot in question (see Using Gtplot in the GWB Essentials Guide).

6.4 Editing plot appearance Gtplot allows you to interactively modify many aspects of the diagram. The details of using active items, aspect menus, and dialogs to edit the plot appearance are given in the Using Gtplot section of the GWB Essentials Guide.

6.5 Scatter data Gtplot can overlay the data in a GSS data sheet (a .gss file) as “scatter data” on a plot of the results of a React calculation. The program can add scatter data to any of the plots it makes, except bar and pie charts. To coordinate the plotting of sample dates and times in the GSS data sheet on the reaction path, set an explicit starting date and time in React. To


read a .gss file into Gtplot, select File → Open → Scatter Data…. Clear scatter data from a diagram on the Open → Scatter Data… dialog, with the OFF button.

The Scatter data section of the Using Gtplot chapter in the GWB Essentials Guide gives details on plotting scatter data from .gss files.

In GWB releases 7.0 and earlier, the program took scatter data from a specially formatted text file, rather than a .gss data sheet. Legacy scatter files are still supported, and are described in the Scatter Data appendix to the GWB Reference Manual.

6.6 Loading and saving plot configuration Upon finishing, Gtplot writes into the user’s working directory a file, “gtplot_conf.gtc”, containing the configuration of the current plots. When the program starts again in the same directory, it reads the file and assumes the same configurations.

Choosing File → Reset Configuration or the reset option from the command line (see Gtplot command line) returns the configuration for each plot type to its default state.

You can also save plot settings in “.gtc” configuration files. To do so, select File → Save As…. You can then specify that file as the configuration for a later Gtplot run from the command line (the -c flag; see Gtplot command line) or read it into Gtplot by selecting File → Open → Configuration….

Exiting the program by choosing File → Abort (No Save) causes an immediate exit from the program; the plot configuration is lost.

6.7 Exporting the plot Gtplot makes it convenient to use the plots you create in articles, reports, presentations, and databases. You can copy the current plot to the clipboard and then paste it into a variety of applications, in a format meaningful to the application.

To copy a plot, use Edit → Copy or Ctrl+C. If you paste the plot into MS PowerPoint, it will appear as an EMF (an MS Enhanced Metafile) graphic object. Pasting into Adobe Illustrator places a native AI graphic.

If you paste the plot into MS Excel or a text editor, such as Notepad or MS Word, the numerical values of the data points that make up the lines on the plot will appear in spreadsheet format.

You can control the format in which the plot is copied to the clipboard by selecting Edit → Copy As. You can choose to copy the plot as an AI object, an EMF object, or a bitmap, or to copy the data points in the plot as tab delimited or space delimited text. Use the tab delimited option to paste the data into a spreadsheet program like MS Excel. For examining the data in a text file created with an editor like Notepad or MS Word, copying from Gtplot using the space delimited option and then pasting into the editor writes a nicely aligned table.

Using Gtplot 139

“Paste” in Excel or Word inserts numerical values


In MS Word or MS Excel, use Paste Special… to paste the plot as a picture instead.

Use File → Save Image… to copy the plot, in your choice of formats (selected under Save as type:), from the graphics area to a file in the specified directory. The Enhanced Metafile option, for example, saves the plot image in a format that can be read by most art and illustration programs (see Graphics Output in the GWB Reference Manual). The other file formats available are: PNG, JPEG, TIFF, Bitmap, Adobe Illustrator, PDF, Scalable Vector Graphics, Compressed SVG, Encapsulated PostScript, Color PostScript, and B/W PostScript.

When saving a PNG, JPEG, TIFF, or bitmap file, you may specify the quality of the saved image by choosing its resolution: High, Medium, Low, or Custom. Use Custom… to set the pixel width and height of the image, and to choose whether to preserve the aspect ratio of the plot. Use the Spreadsheet File (Tab delimited) or Text File (Space delimited) option to save the numerical coordinates of the data points on the plot as a table. The spreadsheet table can be read directly into many popular spreadsheet programs.

Certain graphics types support font embedding. PDF files should always display and print properly, regardless of fonts installed on the system. PostScript files should also, if you have used the option to embed fonts. If you may want to edit the PostScript file, however, you should deselect the option to embed fonts, because programs such as Adobe Illustrator may restrict your ability to edit a document using embedded fonts. To edit these files, be sure that all of the required fonts are installed on your computer (see Font for data markers in the GWB Reference Manual).

“Paste Special…” in Excel or Word

inserts a picture

Using Gtplot 141

When importing AI graphics to Adobe Illustrator, the program may prompt you to update the legacy text before you can edit the file. In this case, choose “Update”. You need to release the clipping mask before you attempt to edit individual elements of the plot. Use the “Ungroup” and “Group” functions when repositioning or modifying elements.

6.8 Gtplot command line To run Gtplot, click on the Gtplot icon on the GWB dashboard, or open a “.gtp” or “.gtc” file. The program can also be initiated from the Windows command prompt by typing gtplot.exe. Starting the program in this way allows you to make use of the command line arguments described below.

Gtplot accepts a number of arguments from the command line. For example, the command

causes Gtplot to read as input the file “React_plot1.gtp”, and to use the plot configuration stored in “Config1.gtc”.

<input_data> -i <input_data>

Set the “React_plot.gtp” dataset, produced by a React run, which contains the data to be plotted. The program, by default, looks for file React_plot.gtp in the user’s working directory.

-c <config_file> Set the configuration file to be read at startup. By default, the program reads the file gtplot_conf.gtc if it exists in the working directory.

-scat <scatter file> Take scatter data from the named dataset. By default, Gtplot does not plot scatter data.

-graph <plot_type> Set the type of plot displayed at startup. By default, it is set from the configuration file. Choose from: xyplot, ternary, piper, durov, schoeller, stiff, radial, bar, pie, series, and time.

-reset Set the default configuration at startup; do not read gtplot_conf.gtc.

gtplot –i React_plot1.gtp –c Config1.gtc


Table 6.1 Keyboard shortcuts in Gtplot

Ctrl+Shift+A Copy plot to the clipboard as Adobe Illustrator AI file

Ctrl+Shift+B Copy plot to the clipboard as a bitmap

Ctrl+C Copy plot to the clipboard

Ctrl+Shift+E Copy plot to the clipboard as an Enhanced Metafile

Ctrl+F Refresh display

Ctrl+Shift+G Get scatter data

Ctrl+L Load a configuration file

Ctrl+M Save the graphic image to a file

Ctrl+O Open an input (“React_plot.gtp”) file

Ctrl+P Print the plot

Ctrl+Q Quit Gtplot, save configuration

Ctrl+Shift+Q Abort Gtplot, do not save configuration

Ctrl+R Reset the plot configuration

Ctrl+S Save the current configuration to a file

Ctrl+Shift+S Copy plot to the clipboard as Spreadsheet (tab delimited)

Ctrl+Shift+T Copy plot to the clipboard as Text (space delimited)

Ctrl+U Update the plot from the current input file

Ctrl+X Reset data range on the x axis

Ctrl+Y Reset data range on the y axis

Ctrl+Z Reset data ranges on the x and y axes

F1 Open online help

143

Using Phase2

Phase2, as described in the Introduction to this guide, is a program designed for calculating a broad variety of two-dimensional diagrams for geochemical systems. The program works by tracing a stacked series of reaction paths that traverse the plot axes, then assembling the results of those paths into a Phase2 diagram.

7.1 Conceptual model A Phase2 calculation has three main components: the initial system, the staging reaction path, and the set of scanning reaction paths.

Phase2 begins a simulation by calculating the system’s initial equilibrium state, which represents the bottom left corner of the diagram.

Beginning from that point, the program traces a staging path that defines the diagram’s left margin. Along the staging path, Phase2 changes the system, just as React does, by adding or removing reactants to vary the system’s composition, changing the temperature, varying the fugacity of gases in an external buffer, and so on.

Starting from intermediate points along the staging path, the program initiates a series of scanning paths that trace a second reaction process. The two-dimensional grid of calculation results makes up the resulting Phase2 diagram, which can be rendered using the P2plot program.


7.2 Staging and scanning paths To configure the staging path, move to the Y Axis pane, where you can set reactants, activity and fugacity buffers, and fixed or varying temperature, much as you would on the Reactants pane in React

In a similar fashion, you move to the X Axis pane to set reactants, buffers, and the temperature trajectory that define the scanning paths

You may equivalently configure the staging and scanning paths from the Command pane. The commands

react y 100 mmol NaCl react x 50 mol CaSO4

Using Phase2 145

set the system’s NaCl content to vary over the staging path, and its CaSO4 composition to vary along the scanning paths.

The scope command lets you specify the target axis for subsequent commands. The commands above might be equivalently entered

To set a polythermal axis, move to the X Axis or Y Axis pane, click the pulldown next to the unit for temperature, and choose “sliding temperature”

Upon selecting this option, two fields are available: “initial temperature” and “slide temperature to”

In this case, the system begins at 25°C and warms to 100°C. The initial temperature represents the left-side temperature on the X Axis pane, or, on the Y Axis pane,

scope y react 100 mmol NaCl

scope x react 50 mmol CaSO4


temperature at the diagram’s lower left. Note the either axis, but not both, may be polythermal in a given run.

From the Command pane, use either the temperature command on a single line

or within a scope block

You control the diagram’s resolution by setting the “Nx” and “Ny” fields on the Config → Output… dialog

or using the “Nx” and “Ny” commands. Note that computing time and memory use increases as the product of the x- and y-direction resolutions, so you should avoid setting overly large values.

When you set a sliding buffer—a sliding pH, pe, Eh, activity, fugacity, or ratio—along one axis, Phase2 automatically sets up the corresponding fixed buffer on the other. To make a “true” Eh-pH diagram, for example, you would set a sliding Eh path on the staging axis, and a sliding pH path on the scanning axis. In this case, the program fixes pH over the staging axis to the left-side value. Then, along each scanning path,

the program picks up Eh at the beginning of the path and holds it constant.

temperature y initial = 25, final = 100

scope y temperature initial = 25, final = 100

Using Phase2 147

To see how this works, set a sliding Eh reactant on the Y Axis pane

then move to the X Axis pane, where the setting “fix Eh” has been automatically applied

While on the X Axis pane, add a sliding pH path

Returning to the Y Axis pane, you will see the “fix pH” setting already applied


Time in Phase2 can vary along only the scanning axis. You can, therefore, define kinetic reactions, use time rates to describe mass transfer, set internal heat sources, and so on, only along the x axis. You may also implement the special model configurations—flow-through, flush, and flash models—only along the horizontal.

Since time advances only along x, kinetic reactions are held at their initial states of disequilibrium everywhere along the staging axis. A mineral that reacts according to a kinetic rate law, for example, neither precipitates nor dissolves as the program traces the staging path. Then, as the program traces the scanning paths, the mineral reacts at the rate specified by its kinetic rate law.

7.3 Progress variables Once Phase2 has completed a calculation, it writes the results to a file “Phase2_plot.p2p”, to be read by the plotting program P2plot. When you start P2plot, the plot axes will be labeled initially in terms of reaction progress. Start configuring your diagram by changing the axis variables to something more meaningful, and choosing whether to display the axes in linear or logarithmic coordinates.

Phase2 passes for each axis a list of potentially meaningful variables—the “progress variables”— to P2plot. The intent in choosing a progress variable along an axis is for its value to be invariant normal to the axis. In other words, scanning from one side of the diagram from a tick mark to the other, the progress variable should not change in value.

In many cases, such invariance is precise only if appropriate units are chosen. For example, if the x axis represents addition of Na+, choosing units of mol gives a diagram in which the axis reads correctly at any point along y. Setting units of mol/kg, on the other hand, might not map precisely if the salinity, and hence kg of fluid, vary along y. To verify validity of a progress variable, simply use P2lot to plot it against the counter-axis.

Each simple reactant is listed as a progress variable such as “Mass reacted, Al+++”. If an original basis entry is added as a simple reactant and its total mass is not affected by other reactants, by charge rebalancing, or by special mass-transfer configurations, the component’s total mass (e.g. “Al+++ in system”) is also listed.

Using Phase2 149

Consider the example

On the x axis, “Mass reacted, Na+” and “Mass reacted, Cl-” are reported as progress variables, as is “Na+ in system”. On the y axis, “Mass reacted, K+” and “Mass reacted, Cl-” are available, along with “K+ in system”. No variable “Cl- in system” is available on either axis, though, because Cl− concentration changes along both axes.

When an axis represents a sliding buffer, the buffered value and its logarithm are each available as a progress variable. If a time span is set for the scanning axis, time is also set as a progress variable. The “Mixing fraction” is listed as a progress variable along the scanning axis for flash models.

Temperature is available as a progress variable for a polythermal axis, for a simple sliding temperature run. For runs accounting for polythermal mixing or internal heat sources, in contrast, temperature is determined by the model, rather than prescribed, and so does not constitute a valid measure of progress along an axis.

7.4 Linear and log stepping You should in general configure Phase2 to step along an axis in a manner that matches how you envision rendering the final plot. If the axis is to be plotted on a linear scale, Phase2 should step along the axis linearly, so that the plot points are evenly spaced along the axis. When an axis variable is to be rendered on a log scale, however, you should set up stepping along the variable’s logarithm.

How you choose between linear and log stepping depends on the variable being rendered on the axis. Most progress variables, such as time, temperature, or mass reacted, step linearly by default, but can be set to vary logarithmically by setting the log argument to the delxi command.

When you set a sliding activity or fugacity reactant (see Sliding activity and fugacity in this guide) activity, fugacity, activity ratio, and fugacity ratio vary linearly, by default. To have Phase2 step along the variable’s logarithm, you constrain the reactant in terms of log units. The pH, Eh, and pe always vary linearly in sliding paths.

In a simulation spanning 100 days, for example, a run with linear stepping might report evenly-spaced results at 0, 50, 100, and so on, days. A run with log stepping, however, might give output at 1, 10, 100, and so on, days. The initial condition, corresponding to 0 days in this example, is not displayed in plots with logarithmic axes.

scope x react 1 mol Na+ react 1 mol Cl-

scope y react 1 mol K+

react 1 mol Cl-


Consider a case in which you want to display the concentration of a component on a logarithmic scale. The commands

will add 0.01 moles of Na+ in the first step (corresponding to Xi = .01), then continue taking log steps until the entire 1 mole has been added. A plot of Na+ reacted might show the variable with evenly spaced ticks at 0.01, 0.1, and 1 mole.

You can combine the delxi and dx_init commands to give detail at the beginning of a path. The commands

will cause the program to add 10−5 moles in the first step (corresponding to Xi = 1e-5), and then proceed with log steps until the entire mole has been added. In this way, a plot of Na+ reacted might show the variable with evenly spaced ticks at 10−5, 10−4, 0.001, 0.01, 0.1, and 1 mol.

You may commonly find need for plotting the “total concentration” of a species (e.g. Na+ in system) as a progress variable, rather than the amount reacted. In this case, the initial concentration (e.g., Na+) specified in the Basis pane should be negligibly small, but nonzero. A value roughly 4 orders of magnitude smaller than the value corresponding to the first step works well. A constraint of 10−6 mol Na+ would work well for the first example described above, but 10−9 mol might be used for the second example.

7.5 Settable variables Phase2 allows you to alter the values of certain variables carried in the calculation. Table 7.1 lists variables that differ from those carried by React (see Table 2.1), along with their units and default values.

scope y react 1 mol Na+ delxi .01 log

scope y react 1 mol Na+ delxi .01 log dx_init = 1e-5

Using Phase2 151

Table 7.1 Settable variables in Phase2 differing from React, their units and default values

Pane or Dialog Variable Default Unit Description Output dxprint x | y .1 – Interval between printing

results.

Nx, Ny 301, 301 – Number of data points in the plot grid

Stepping delxi x | y .01 – Step size in reaction progress, log/linear stepping.

dx_init x | y not set – Initial step size in reaction progress.

step_increase x | y

1.5 – Maximum proportional increase in step size.

step_max x | y not set – Number of reaction steps the program may take in any single path.

threads equal to number of cores

– Number of threads to spawn, for parallel execution.

To change a variable, type the new value on the Basis or Medium pane or in the dialog boxes under Config, or enter as a command the variable name followed by the new value. Examples:

Variables accepting an x or y argument can alternatively be set within a scope block:

Nx = 101 delxi y = 0.1 log dx_init y = 1e-10

scope y delxi = 0.1 log dx_init = 1e-10


Values are entered in the units carried internally by the program, as listed in Table 2.1 or Table 7.1. To restore a variable to its default value, enter a blank field in the dialog box, or on the Command pane type its name without a value or followed by a ”?”:

Current settings can be viewed at any time on the relevant dialog box, or using the command show variables.

7.6 Multicore execution Phase2 is multithreaded in such a way that multicore computers trace the scanning paths in parallel. Like X1t and X2t, described in the GWB Reactive Transport Modeling Guide, you can control the number of threads Phase2 spawns on the Config → Stepping… dialog, or with the threads command.

From the same dialog, or with the pluses command, you can control the amount of output shown on the Results pane after each step. Like X1t and X2t, Phase2 reports upon completion of a calculation the computing time needed to execute parallel and serial sections of the code, as well as the clock time elapsed over the run.

7.7 Running a model Once you have configured a simulation, you are ready to run it. A number of example input files for Phase2 are installed with the GWB Professional package, in subdirectory “Script” within the installation directory (e.g., in “\Program Files\GWB\Script”). The example files have “.ph2” extensions. To give the program a test drive, double-click on one of the files.

Start the simulation in any of several ways: selecting Run → Go, pressing Ctrl+G, typing go on the Command pane, or clicking the Run button on the Results pane. You can watch on the Results pane as the model follows the simulation procedure, first computing the initial conditions, then tracing the staging reaction path, and finally tracing each scanning reaction path.

When the calculation is complete, click on the Plot Results button to launch P2plot. This program lets you render the simulation results graphically, as two-dimensional diagrams, in which you render the results as maps of species predominance or mineral assemblages. You can also color map and contour any variable. Additionally, you can plot cross-sections through the diagram. The chapter Using P2plot in this guide gives further details.

You can have the model produce text-format or “print” results describing the chemical state, along with the isotopic state, if applicable, at each stage of the calculation. To do so,

Nx Nx = ?

Using Phase2 153

select Config → Output… and then select the “print dataset” option. The program will write results at intervals in the reaction progress (ξ) set by variable “dxprint” on the Config → Output… dialog. When the model is complete, click on View Results. The print option can produce large amounts of output and, therefore, is by default turned off.

After finishing a simulation, you can revise the model configuration and run it again. When the new simulation is complete, any instances of P2plot running on your computer will automatically update their plots to reflect the latest results. You can open several P2plot windows on your computer at the same time, allowing you to view results plotted in different ways.

By clicking on Run → Go Initial or typing go initial, you cause the program to evaluate the initial conditions without tracing either the staging or scanning reaction paths. You can also click on Run → Go Y or type go y to trace the staging path (the left edge of the diagram). Similarly, click on Run → Go X or type go x to trace a single scanning path (the bottom edge of the domain). Once done, you can render the initial conditions with P2plot, as you could the results of any simulation. These features are handy because they let you verify that the initial system or either reaction path is set up correctly, without completing the entire simulation.


7.8 Example: Speciation diagram As a first example, we construct a “true” fO2-pH diagram for the copper-sulfur-water system at 250°C. Double-click on file “CuSH2O.ph2” to launch Phase2 and move to the Basis pane

Here we constrain the chemical system at the bottom-left corner of the diagram: the background electrolyte is 50 mmol/kg NaCl, and the fluid contains 1 mmol/kg sulfur and 10 μmol/kg copper. The corner marks a log fugacity of −50 and a pH of 3.

The Y Axis pane sets up the staging axis

Using Phase2 155

such that the logarithm of oxygen fugacity slides to 5, while pH holds constant. In contrast, the X Axis pane

fixes fugacity, but slides pH to 11. You can alternatively use the commands

from the Command pane to configure the same calculation. Move to the Results pane and click to trigger the calculation. When the

program finishes, choose to open dataset “Phase2_plot.p2p”, which holds the calculation results, in program P2plot.

In P2plot, select Plot → 2D Diagram. When the diagram displays, double-click on one of the axis variables (or go to Format → Axis Range and Variables…) and on the X Axis tab set “Progress Variable” to “pH”

T = 250 C

Na+ = 50 mmol/kg Cl- = 50 mmol/kg balance on Na+

swap HS- for SO4-- HS- = 1 mmol/kg Cu+ = 10 umol/kg

swap O2(g) for O2(aq) O2(g) = -50 log fugacity pH = 3

scope y slide log fugacity of O2(g) to 5 scope x slide pH to 11


Then, on the Y Axis tab, set the variable for the y axis to “log f O2(g)”. Next, click on Format → Predominance Map… to expose the Predominance Map

dialog. Check the box next to “Predominance Map”, if it is not already, and next to “Variable to map” choose “Cu+”

Click on Apply.

Using Phase2 157

The resulting diagram shows the predominant copper-bearing species and minerals at 250°C as a function of pH and oxidation state

The plot is truncated at low and high fO2 by the upper and lower stability limits of water. To extend the diagram, return to the Predominance Map dialog, uncheck “Truncate”, and click on Apply. To diagram predominant sulfur-bearing species, return to the dialog, change the “Variable to Map” to “SO4--", and once again hit Apply.


7.9 Example: Mineral solubility The input file “AlSolubility.ph2” calculates the solubility of aluminum in the presence of quartz as a function of pH and the system’s aluminum content. Double-click the file to launch Phase2. The Basis pane

describes the starting point for our calculation, a pH 3 fluid in equilibrium with quartz at 100°C. The fluid carries a near-zero mass of dissolved aluminum. We don’t include a background electrolyte, so charge balancing is disabled.

The Y Axis pane

shows the staging path, along which 10 µmol of Al+++ is titrated into to the system, while pH is held constant. On the X Axis pane

Using Phase2 159

pH is set to slide from 3, the starting point, to a final value of 8. On the Config → Stepping… dialog

we set logarithmic stepping along the y axis, with an initial step size of 10−4. Since we’re ultimately adding 10−5 moles of Al+++, Phase2 will add 10−4×10−5 = 10−9 moles to the initially negligible mass on the first step, then exponentially larger aliquots as it takes subsequent steps.

Press the button on the Results pane to trace the calculation. Start P2plot by clicking on the button and select Plot → 2D Diagram. Double-click on the x axis label and set “Progress Variable” to “pH”. Move to the Y axis tab and set “Progress Variable” here to “Al+++ in system” with a log scale. Adjust the tick increment on each axis, if you wish, by de-selecting “Auto-scale”, and click OK.

Next, select Format → Assemblage Map…, check the box at the top of the dialog, and click OK. Select Format → Contour Map… and check the box at the top of the dialog. Next to “Variable type”, choose “Components in fluid”, set “Variable to contour” to “Al+++”, and for “Variable units”, set “umol/kg”. Make sure “Type of plot” is “Log”, adjust the point size and color of the contour lines to your liking, and click OK.


The resulting diagram

delineates the stability of kaolinite in the presence of quartz, and contours the logarithm of aluminum solubility, in μmol/kg.

Using Phase2 161

7.10 Example: Oxygen solubility In this example we diagram the solubility in water of atmospheric O2(g) as a function of salinity and temperature. Our strategy is to define a dilute fluid in equilibrium with the atmosphere at 0°C to occupy the lower-left corner of the diagram. We will then set temperature to increase along the staging axis, and salinity along the scanning axis, while holding O2(g) fugacity constant across both axes.

Begin by double-clicking on file“O2Solubility.ph2” to launch Phase2. The Basis pane

sets the bottom left corner of the diagram, whereas the Y Axis pane

slides temperature along the staging path, and the X Axis pane


sets up a titration of 3 mol of Na+ and Cl− as simple reactants along the scanning paths. The simulation, then, consists of a series of isothermal titration paths, each traced at

fixed oxygen fugacity, and each maintaining the temperature of its point of departure from the staging path. Press the button on the Results pane to trace the calculation.

Press to launch P2plot, then select Plot → 2D Diagram. Double-click on one of the axis variables (or go to Format → Axis Range and Variables…), then set the x axis progress variable to “Na+ in system”, with units of “mmol/kg”, and the y axis variable to “Temperature”. Now, select Format → Contour… to expose the contour plot dialog. Choose “Species concentrations”, “O2(aq)”, “mmol/kg”, and “Linear” in the top four fields, then check the box next to “Contour Lines” and click on Apply. Under Format → Color Map…, choose the same settings and hit Apply.

Using Phase2 163

The resulting diagram shows how oxygen solubility decreases with increased temperature and salinity

The diagram reflects how the log K of the reaction between O2(g) and O2(aq) decreases with temperature, while the activity coefficient of O2(aq) increases with ionic strength. The latter effect is commonly known as the “salting out” effect.


7.11 Example: Isotope fractionation In this example, we diagram the 13C composition of CO2(g) in equilibrium with a carbonate-bearing fluid of known carbon isotopic composition, as a function of pH and temperature. Double-click on file “CO2_frac.ph2” and when Phase2 opens, move to the Basis pane

Here, the lower-left corner of the diagram is a carbonate solution at pH 4 and 0 °C. Since we are not concerned with the background electrolyte, we disable charge balancing.

The Y Axis pane

sets a polythermal staging axis in which temperature increases linearly to 150°C.

Using Phase2 165

On the X Axis pane

we slide pH to 10, while holding temperature constant. On the Config → Isotopes… dialog

we set δ13C of the fluid to −20 ‰ PDB. There is in the simulation no external source or sink of 13C, and no mineral precipitates, so the fluid’s bulk isotopic composition remains constant across the diagram.

Press the button on the Results pane to trace the calculation. Start P2plot by clicking on the button. In P2plot, select Plot → 2D Diagram, then click on Format → Axis Range and Variables… to set the axis variables to “pH” along the x and “Temperature” along the y axis.

Next, click on Format → Color Map… and check the box on the top line. Next to “Variable type”, choose “Isotopic composition 13-C” and then set “Variable to map” to “CO2(g)”. Adjust the colors as you like and click OK. Now, open the Format → Contour… dialog, make the same settings for “Variable type” and “Variable to map”, set the appearance options to your liking, and again click OK.


P2plot at this point should display a diagram similar to

As we see, the isotopic composition of CO2(g) in equilibrium with the fluid varies with pH in response to the changing balance between CO2(aq) and the carbonate species HCO3

− and CO3

−−, and along the vertical axis as the isotopic fractionation factors shift with temperature.

Using Phase2 167

7.12 Example: Surface complexation Input file “ZnSorption.ph2” sets up calculation of a diagram showing the controls of pH and Zn++ content on the metal ion’s surface complexation with ferric hydroxide. Double-click the file to launch Phase2 and move to the Basis pane

which sets at the bottom-left of the diagram a NaCl solution containing a small amount of Zn++, in contract with ferric hydroxide. Note on the Config → Redox couples… dialog that the Fe+++/Fe++ couple has been disabled, allowing us to carry ferric iron as a basis entry.

On the Y Axis pane


Zn++ is titrated into the system while pH is held constant. The X Axis pane

slides pH from its initial value of 4 at the left of the diagram, to 12 at the right. On the File → Open → Sorbing Surfaces… dialog

we see that the Dzombak and Morel dataset for ion complexation with hydrous ferric oxide is loaded.

Using Phase2 169

On the Config → Iteration… dialog

the “precipitation” option has been unchecked, preventing new minerals from forming during the simulation. Finally, the “sorbate” option here has been checked, specifying that the concentration of Zn++ set on the Basis pane represents the sum of the basis entry’s dissolved and sorbed masses.

Press the button on the Results pane to trace the calculation, then start P2plot by clicking on the button. In P2plot, select Plot → 2D Diagram. Then, on the Format → Axis Range and Variables… dialog, set “pH” on the x and “Zn+++ in system” on the y axis, and click OK. Select Format → Predominance Map… and choose “Zn++” for “Variable to map”, then hit Apply. Go to Edit → Contour… , check the box at the top, and choose “Sorbed fractions” for “Variable type”, and “Zn++” for “Variable to contour”. Make sure to select a “Linear” mapping, set the appearance and contour interval to your liking, and hit Apply.


The resulting diagram should look like

As is typical of a divalent metal, Zn++ does not sorb at low pH. Under neutral to alkaline conditions, the strong sites account for most of the sorbed Zn++ where the system contains little Zn++. At higher zinc contents, however, the weak sites hold most of the zinc in the system, due to their greater abundance relative to the strong sites. Along the top of the diagram, the capacity of the ferric hydroxide to hold zinc is overwhelmed, and most of the metal is found in solution.

Using Phase2 171

7.13 Example: Kinetic diagram The input file “Promoting.ph2” builds on a React calculation borrowed from the section Kinetics of redox reactions in the Kinetic Reaction Paths chapter of this manual. In that example, contained in dataset “Redox.rea”, ferrous iron oxidizes to ferric hydroxide according to a kinetic rate law. In the rate law, OH− promotes the oxidation reaction with a power of 2.

In this section, we construct a Phase2 diagram showing how pH, which controls OH− concentration, affects the oxidation rate. Opening “Promoting.ph2”, the Basis pane

is much like that in the React example, except the pH is set slightly lower, to 6.7.


The Y Axis pane

sets up a staging path along which pH varies from its initial value at the bottom of the diagram to 7.3 at the top. The fluid is to remain in equilibrium with the atmosphere, so oxygen fugacity needs to be buffered here, as well as on the X Axis pane.

The settings on the X Axis pane

fix pH according to the departure point on the staging path, define the kinetic rate law, and hold oxygen fugacity constant. The rate law entry, once expanded, is unchanged from the React example; notably, OH− serves as a promoting species.

Press the button on the Results pane to trace the calculation, then start P2plot by clicking on the button. Select Plot → 2D Diagram, set the x axis variable to “Time” in days, and the y axis to “pH”.

Using Phase2 173

Open the Format → Predominance Map… dialog. Change the “Variable type” pulldown from “Basis species” to “Element”, select “Iron” as the “Variable to map”

and hit Apply. Set in this way, the predominance diagram will include both ferrous and ferric iron-bearing species and mineral.

Open the Format → Contour… dialog and check the box at the top. Choose “Reactant properties” for “Variable type”, and for “Variable to contour, select “Reaction rate, redox-1 (x)”. Set “Variable units” to “mmol/kg/day” and, for “Type of plot”, set “Log”. Choose appearance options and a contour increment to your liking, and press Apply.


The diagram should look something like

As reflected by the contours of log reaction rate, reaction proceeds faster as pH increases, reflecting the role of the hydroxyl ion as a promoting species in the kinetic rate law. Along x, the reaction slows with time as another promoting species, the Fe++ ion, is depleted over time.

Using Phase2 175

7.14 Cross-section plots P2plot can diagram cross-sections through any diagram. You makes x-y plots of a broad range of variables such as pH, species concentration, mineral mass, gas pressure, isotopic composition, and so on.

To plot along a cross-section, select Plot → Cross-section Plot… to expose the configuration dialog. On the X Axis pane, choose the section’s orientation by setting “Orientation” to either “Along scanning paths” or “Across scanning paths”. On the Y Axis pane, if the orientation is along the scans, set “Display” to “Several values at one step along y” or “One value at several steps along y”. Plotting across the scans, the choices both read “… along x”.

Now, on the X Axis pane, select a category from the “Variable type” dropdown and choose the x-axis variable from the list. Similarly, set “Variable type” on the Y Axis pane. At this point, depending on the “Display” setting, you can choose either several variables on this pane and a single step on the Step axis, or one y-axis variable and several steps.

As an example, re-run file “ZnSorption.ph2”, launch P2plot, and select Plot → Cross-section Plot…. On the X Axis pane, set “Orientation” to “Along scanning paths” and choose to plot “pH” among the “Chemical parameters”; under Y Axis, set “Variable type” to “Species concentration”, “Filter” to “Zn++”, “Display” to “Several values at one step along y”, and then set a “linear” scale. Click on Select all, if necessary. Moving to the Step pane, set “Progress variable” to “Zn++ in system”, set the unit to “mmol”, and choose “Zn++ in system = .1 mmol”.

The resulting plot should look like


Here, the Zn++ ion is present in free form under acidic conditions, but complexed with strong and weak sites on the ferric surface at neutral to alkaline pH.

We can alternatively plot one variable at several points along the staging axis. Return to the Y Axis pane, set “Display” to “One value at several steps along y” and then “Variable type” to “Sorbed fractions”. On the Step pane, choose “Zn++ in system = 1 mmol”, hold down the Ctrl key while selecting the corresponding entries for “… 2 mmol” and “… 3 mmol”, and click Apply.

The resulting plot should look like

As more Zn++ is added to the system, a lesser fraction of it sorbs to the ferric hydroxide. As a final example, we make a vertical section through the diagram. Returning to the

X Axis pane, change “Variable type” to “Components in fluid”, set “Orientation” to “Across scanning paths”, and choose “Zn++” from the list. On the Y Axis pane, set “Variable type” to “Components in sorbate” and again choose “Zn++” from the list.

On the Step pane, set “Progress variable” to “pH” and choose the pH values closest to 5, 6, 7 and 8, then click on Apply. The resulting plot

Using Phase2 177

shows the Zn++ sorption isotherms at the pH values of interest.


7.15 Phase2 command line You can start Phase2 by clicking the icon under the “Start” menu, opening a “.ph2” file, or entering the command phase2.exe from the Windows “Command Prompt”. When you start Phase2 from the command line (as opposed to clicking on the icon), you can specify a number of arguments. For example, the command

causes Phase2 to read input commands from a file “my_script”, and to use “my_thermo.tdat” as the thermodynamic database.

The following options are available from the command line: -cd Change the working directory to the directory

containing the input script specified with the –i option.

-nocd Do not change the working directory.

-i <input_script> Set a file from which to read input commands.

-gtd <gtdata_dir> Set directory to search for thermodynamic datasets.

-cond <cond_data> Set the dataset for calculating electrical conductivity.

-d <thermo_data> Set the thermodynamic dataset.

-iso <isotope_data> Set the dataset of isotope fractionation factors.

-s <surface_data> Set a dataset of surface sorption reactions.

phase2 –i my_script –d my_thermo.tdat

179

Using P2plot

P2plot is a graphics program that produces various types of diagrams showing the results of Phase2 calculations. The program is similar to Gtplot and Xtplot, so if you have familiarized yourself with these programs, you already know much of what you need to know to run P2plot.

After running Phase2, start P2plot by clicking on Plot Results on the Results pane, or selecting Run → P2plot from Phase2’s menubar. The program will read the calculation results from the “.p2p” file Phase2 produced and render them graphically. You can leave P2plot active when you run further Phase2 simulations. Each time Phase2 completes a run, it signals P2plot, which updates its display to reflect the new results.

You can also start P2plot by opening any “.p2p” or “.p2c” file, or by clicking on the P2plot icon on the Apps pane of the GWB dashboard. You can take input from a different dataset by dragging the dataset into the P2plot window, or choosing File → Open → Data File… from the menubar. Depending on the plot you choose, P2plot might look like

Fe(OH)2

Fe(OH)2+

Fe(OH)3(ppd)

Fe(OH)4-

Fe++

FeCl++

FeOH+

FeOH++

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P2plot produces plots of various types. You can generate a two-dimensional rendering of the results, showing the predominant form of any original basis species or element, or a map of mineral assemblages. You can also show one or several variables represented by color shading or contours.

Alternatively, you can plot cross-sections through the diagram that show how certain variables change with reaction progress along staging or scanning paths. You can plot one or more variables from a single section, or one variable from several cross-sections.

Choose the diagram type from the Plot pulldown on the menubar. The program can render the following types of variables:

Mass and volume of minerals in the modeled system Concentration, activity, and activity coefficients of dissolved species Elemental composition of the fluid, minerals, sorbate, and the bulk system Composition of the fluid, minerals, sorbate, and the bulk system, expressed in

terms of thermodynamic components Gas fugacity and partial pressure Saturation indices Q/K with respect to various minerals Bulk stable isotopic composition of the fluid, minerals, sorbate, and the entire

system, as well as the composition of individual species, gases, and minerals Fraction of various components sorbed onto mineral surfaces Variables such as temperature, pH, and reacted mass

When P2plot starts for the first time in a given directory, it assumes a default configuration. Upon finishing, the program saves for its next run a dataset containing the current configuration of the plots. You can select options from the File menu to specify an alternative configuration (see Loading and saving plot configuration) or to reset the entire program configuration.

8.1 2D Diagram P2plot makes two-dimensional diagrams, in which variables are represented by color shading, color masking, and contour lines. You can plot species’ fields of predominance, or mineral assemblages. For two-dimensional plots, the Format menu contains a number of configuration options Quick Toggle… to select the graphical elements of the plot to display Color Map… to define a shaded color map of a variable over the diagram axes Color Mask… to color mask of a variable’s value range over the diagram axes Contour… to choose a variable to contour and configure the contouring Predominance Map… to plot the species accounting for the most mass of any

original basis species or element Assemblage Map… to plot fields representing every mineral or combination of

minerals over the diagram axes

Using P2plot 181

Appearance… to open a tabbed dialog containing the following: o Axes and Ticks… to define the appearance of the coordinate axes o Plot Area… to choose the dimensions, placement, and background color

of the plot o Title… to define a title for the plot o Font… to control aspects of the text throughout the diagram

Axis Range and Variables… to select the two variables appearing on the diagram’s axes and adjust the tick increment

Side Banner… to specify the appearance and placement of the informational banner along the side of the plot

GSS Data… to affect the labeling of scatter data loaded from a GSS spreadsheet and the related legend

Alternatively, you can interactively modify many aspects of the plot, including lines, labels, axes, scales, and grid lines. A right-click on an aspect displays a menu showing the options available. A double-click on an aspect brings up a related dialog. Left-click on an aspect to select it for modification.

An aspect has been selected when its color changes, as in the case of lines, or when it is surrounded by manipulation handles, in the case of text, markers, and scales. Change the size of text, markers, scales, and the plot itself by dragging the sizing cursors. Adjust the placement of the plot by clicking within the plot or on either axis and dragging it. The plot title can be moved in the same way.


8.1.1 Predominance Maps A predominance map shows the aqueous species, surface species, or mineral that accounts for the greatest mass of any component or element. A gas predominates if its partial pressure exceeds the confining pressure, which corresponds to the temperature.

Use the Predominance Map… dialog to control aspects of the map. First select the species you’d like to diagram. Sort by thermodynamic components by selecting “Basis species”

Left-click edge and drag to resize plot

Double-click background to show Quick Toggle dialog

Hover to view data values

Double-click aspects to configure Predominance

Map view

Left-click axis and drag to move plot

Right-click aspects to configure 2D diagram

Using P2plot 183

or by elements by selecting “Element”

In many cases the resulting diagrams will be identical, but the latter option is especially useful for plotting decoupled redox species together.

You can hover on the plot to see the number of moles of the selected basis entry or element in the predominant species. For a gas, the partial pressure is reported.

By default all types of species are considered in the diagram, but you can hide any class by unchecking the appropriate box. In the example below

>(w)FeOHSeO3--

>(w)FeSeO3-

FeSe2

H2Se

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Se(black)

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aqueous species, surface species, and minerals predominate at some point. Uncheck “Mineral Fields”

to ignore them in the tabulation of most abundant species. Predominance maps by default draw lines representing the stability region of water

and do not display species outside this region. Water is treated as unstable anywhere the partial pressure of O2(g) or H2(g) exceeds the confining pressure corresponding to the temperature of the calculation. Uncheck “Water Limits”

>(w)FeOHSeO3--

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H2Se

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HSeO3-

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to ignore the stability limits. Or, with “Water Limits” checked, uncheck “Truncate” to draw outside the stability limits.

The Tables section of the thermo dataset shows the pressure corresponding to each of the principal temperatures. The Thermo Datasets Appendix to the GWB Reference Manual describes thermo datasets and the GWB Essentials Guide includes a description of the TEdit app used to view and modify the datsets.

Each type of field (Aqueous, Surface, Mineral, Gas) is colored differently by default. All minerals, for example, are colored a light orange (“Old lace”). Click on the colored square next to a species type (e.g. All minerals) to change the color for that field. To set the color of an individual species, select it from the pulldown, then pick a color. To change the color of elemental selenium, for example, change the pulldown next to “Mineral Fields” from “All minerals” to “Se(black)”, then click on the color box to pick a color.

>(w)FeOHSeO3--

>(w)FeSeO3-

FeSe2

H2Se

H2SeO

3

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HSeO3-

Se(black)

SeO3--

SeO4--

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The FeSe2 keeps its original color, but the Se(black) field has been updated. You can additionally change the color and thickness of lines separating species, as well

as the water stability limits, and the size, color, and style of labels.

8.1.2 Assemblage Maps Assemblage maps show fields in which a mineral or group of minerals exist in the calculation. You can hover over any field to see the assemblage of minerals present. Where no minerals form, the hover text displays “No minerals”.

Use the Format → Assemblage Map… dialog to control aspects of the diagram. All assemblages plot in the same color by default, but you can color assemblages individually, in the same way described above for predominance fields.

Depending on the number of unique mineral assemblages present in a calculation, and the number of minerals defining each assemblage, assemblage maps can become quite crowded. Use the “Label type” pulldown to control whether full names, shortened names, or a number representing each assemblage labels each field. You can remove the labels entirely by unchecking the “Labels” box. A legend, which you can toggle on or off with the

>(w)FeOHSeO3--

>(w)FeSeO3-

FeSe2

H2Se

H2SeO

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Se(black)

SeO3--

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“Legend” box, lists each assemblage present and displays the field color, abbreviations, and/or index for each assemblage. In the example below

the “Shortened names” option is chosen to simplify the assemblage labels. The legend lists each assemblage as it appears on the plot and defines each abbreviation.

) Gro + Qua) Kao + Qua) Lau + Qua) Max + Qua) Mus + Qua) Pre + Qua

Gro = GrossularKao = KaoliniteLau = LaumontiteMax = Maximum MicroclineMus = MuscovitePre = PrehniteQua = Quartz

Gro + Qua

Kao + QuaLau + Qua

Max + Qua

Mus + Qua Pre + Qua

12 13 14 15 16 17 18 19 202

3

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7

8

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log ratio Ca++/H+^2

log

ratio

K+ /

H+

Asse

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8.1.3 Axis Variables A 2D diagram’s axes by default are labeled in terms of reaction progress, which has meaning only in terms of how the calculation is set up. Use the Format → Axis Range and Variables… dialog to control the variables appearing on the x and y axes, their units where applicable, and to set custom ranges and tick increments. For more information, see Progress variables in this guide.

8.2 Cross-section Plot configuration You can plot one or more horizontal or vertical cross-sections through the calculated 2D diagram. Horizontal sections represent progress along the scanning paths, while vertical sections represent progress across the scanning paths.

Choose Plot → Cross-section Plot… to configure a cross-section plot. You can alter the configuration by interacting with the graphical aspects of the plot, such as any data line, data label, axis, tick mark, label, or grid line. A right-click on an aspect of the plot displays a menu showing the options available. Double-click on an aspect to invoke the Cross-section Plot Configuration dialog. Dragging an inner or outermost axis tick mark, number, or grid line will shift or scale, respectively, the axis range, (see Using Gtplot in the GWB Essentials Guide).

The X Axis tab lets you specify whether a horizontal or vertical cross-section is shown. The default x-axis setting is reaction progress in the x direction (a horizontal section). Use the Orientation pulldown to control the orientation of the cross-section.

The X Axis tab also lets you select the variable to appear on the x axis. Most commonly you would choose the variable or variables representing reaction progress (see Progress variables in this guide), but a cross-section plot, like an XY plot in Gtplot, can plot any variable on the x axis. For this reason, progress variables are not listed separately from the larger set of variables. Use Variable type to control the type of variables to appear along the x axis. Variable type options are:

Using P2plot 189

Chemical parameters such as temperature, pH, and mass solution Physical parameters such as fluid density, porosity, and fluid velocity Reactant properties such as net reaction progress and reaction rates Components in the fluid, minerals, sorbate, and the bulk system (fluid plus

sorbate and rock) Component Kd’s of the various components that may be sorbed onto mineral

surfaces Sorbed fractions of the various components that may be sorbed onto mineral

surfaces Species to plot either the concentration, activity, or activity coefficient of one or

more aqueous species Minerals to represent the masses or volumes of minerals over the reaction path Mineral Saturation to plot the saturation indices (Q/K) of the fluid with respect to

one or more minerals Gas partial pressure and Gas fugacity of one or more gases in the fluid Elemental Composition of the fluid, the rock, the sorbate (i.e., surface

complexes), or the system (fluid plus sorbate and rock) Isotopic composition of the bulk fluid, rock, sorbate, and system, as well as

individual species, for active isotope systems The selection of a variable type displays a list of possible variables. Click on a variable

you wish to select. Use the following to specify the way the variables are plotted: Variable type to control the type of variables to appear along the plot’s axis Consider to list, for species or mineral saturation plots, the set of just those that

contain a given basis species Auto-scale to set the data range for the axis to span the data to be plotted Minimum, Maximum, and Tick increment to set the data range for the axis Reverse axis to reverse the sense of the axis Units to select alternative units, if any, for the axis As to plot values as elemental equivalents, or as protonated or deprotonated

species equivalents Type to set the axis to a linear, log, or delta scale. A delta scale shows change in

a variable’s value from the initial point in any particular step First, Previous, Next, and Last to cycle through the variable choices


The Y Axis tab lets you select the variables to plot on the y axis and specify the way they are plotted. Choose a Variable type and variable just as you do on the x axis. Use the Filter menu to set, for species or mineral saturation plots, a basis species to consider. In a typical calculation, so many dissolved species are considered, and saturation states are determined for so many minerals, that the data fit poorly on a single plot. For this reason, P2plot can group species and minerals into sets of just those that contain a given basis species. You can choose to plot, for example, the species containing Na+, or the saturation indices of minerals containing Al+ + +. Alternatively, you may choose to consider all species and minerals.

The selection of a variable type displays a list of possible variables. Click on a variable you wish to select. Use Ctrl+click to select multiple variables. Use Shift+click to select a range of variables.

The Step tab lets you select the position in the diagram for which data should be rendered. If you are plotting a horizontal section (a scanning path), the step indicates reaction progress along the vertical direction (the staging path). If you are plotting a vertical section (the staging path, or parallel sections), the step indicates progress along the horizontal direction (the scanning path).

Depending on how the calculation is configured, one or more descriptive progress variables may be available. Use the Progress variable pulldown to choose from the available options. The progress variable aids in step selection and is used to label cross-section plots.

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Use the First, Previous, Next, and Last buttons to cycle the plot through the steps. You can choose from the Y Axis or Step tab to display several values from a single step,

or one value from several steps.

8.3 Plot types Use the Plot menu to choose between the 2D Diagram View and the Cross-section Plots. Each selection invokes a dialog box specific to the type of plot in question (see Using Gtplot in the GWB Essentials Guide).

8.4 Editing plot appearance P2plot allows you to interactively modify many aspects of the diagram. The details of using active items, aspect menus, and dialogs to edit the plot appearance are given in the Using Gtplot section of the GWB Essentials Guide.

8.5 Scatter data P2plot can overlay the data in a GSS data sheet (a .gss file) as “scatter data” on a plot of the results of a Phase2 calculation. The program can add scatter data to any of the 2D


diagrams it makes, as well as the cross-section plots. To coordinate the plotting of sample dates and times in the GSS data sheet on the reaction path, set an explicit starting date and time in Phase2.

To read a .gss file into P2plot, select File → Open → Scatter Data…. Clear scatter data from a diagram on the Open → Scatter Data… dialog, with the OFF button. The Scatter data section of the Using Gtplot chapter in the GWB Essentials Guide gives details on plotting scatter data from .gss files.

In GWB releases 7.0 and earlier, the program took scatter data from a specially formatted text file, rather than a .gss data sheet. Legacy scatter files are still supported, and are described in the Scatter Data appendix to the GWB Reference Manual.

8.6 Loading and saving plot configuration Upon finishing, P2plot writes into the user’s working directory a file, “p2plot_conf.p2c”, containing the configuration of the current plots. When the program starts again in the same directory, it reads the file and assumes the same configurations.

Choosing File → Reset Configuration or the reset option from the command line (see P2plot command line) returns the configuration for each plot type to its default state.

You can also save plot settings in “.p2c” configuration files. To do so, select File → Save As…. You can then specify that file as the configuration for a later P2plot run from the command line (the -c flag; see P2plot command line) or read it into P2plot by selecting File → Open → Configuration….

Exiting the program by choosing File → Abort (No Save) causes an immediate exit from the program; the plot configuration is lost.

8.7 Exporting the plot P2plot makes it convenient to use the plots you create in articles, reports, presentations, and databases. You can copy the current plot to the clipboard and then paste it into a variety of applications, in a format meaningful to the application.

To copy a plot, use Edit → Copy or Ctrl+C. If you paste the plot into MS PowerPoint, it will appear as an EMF (an MS Enhanced Metafile) graphic object. Pasting into Adobe Illustrator places a native AI graphic.

If you paste the plot into MS Excel or a text editor, such as Notepad or MS Word, the numerical values of the data points that make up the lines on the plot will appear in spreadsheet format.

You can control the format in which the plot is copied to the clipboard by selecting Edit → Copy As. You can choose to copy the plot as an AI object, an EMF object, or a bitmap, or to copy the data points in the plot as tab delimited or space delimited text. Use the tab delimited option to paste the data into a spreadsheet program like MS Excel. For

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examining the data in a text file created with an editor like Notepad or MS Word, copying from P2plot using the space delimited option and then pasting into the editor writes a nicely aligned table.

8.8 P2plot command line To run P2plot, click on the P2plot icon on the GWB dashboard, or open a “.p2p” or “.p2c” file. The program can also be initiated from the Windows command prompt by typing p2plot.exe. Starting the program in this way allows you to make use of the command line arguments described below.

P2plot accepts a number of arguments from the command line. For example, the command

causes P2plot to read as input the file “Phase2_plot1.p2p”, and to use the plot configuration stored in “Config1.p2c”.

-i <input_data> Set the “Phase2_plot.p2p” dataset, produced by a Phase2 run, which contains the data to be plotted. The program, by default, looks for file Phase2_plot.p2p in the user’s working directory.

-c <config_file> Set the configuration file to be read at startup. By default, the program reads the file p2plot_conf.p2c if it exists in the working directory.

-scat <scatter_file> Take scatter data from the named dataset. By default, P2plot does not plot scatter data.

-graph <plot_type> Set the type of plot displayed at startup. By default, it is set from the configuration file. Choose from: 2d and cross-section.

-reset Set the default configuration at startup; do not read p2plot_conf.p2c.

p2plot –i Phase2_plot1.p2p –c Config1.p2c

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Appendix: Further Reading

The following literature references, from the many hundreds that have been published, provide a starting point for further reading on various aspects of geochemical modeling and its applications. Additional references are available in the GWB Essentials Guide and the GWB Reactive Transport Modeling Guide.

A.1 Reaction modeling Bethke, C.M., 2008, Geochemical and Biogeochemical Reaction Modeling. Cambridge

University Press, New York, 547 p. Garrels, R.M. and F.T. MacKenzie, 1967, Origin of the chemical compositions of some

springs and lakes. In Equilibrium Concepts in Natural Waters. American Chemical Society, Advances in Chemistry Series 67, 222–242.

Helgeson, H.C., 1968, Evaluation of irreversible reactions in geochemical processes involving minerals and aqueous solutions—I.Thermodynamic relations. Geochimica et Cosmochimica Acta 32, 853–877.

Helgeson, H.C., R.M. Garrels and F.T. Mackenzie, 1969, Evaluation of irreversible reactions in geochemical processes involving minerals and aqueous solutions—II. Applications. Geochimica et Cosmochimica Acta 33, 455–481.

Helgeson, H.C., T.H. Brown, A. Nigrini and T.A. Jones, 1970, Calculation of mass transfer in geochemical processes involving aqueous solutions. Geochimica et Cosmochimica Acta 34, 569–592.

Parkhurst, D.L., D.C. Thorstenson and L.N. Plummer, 1980, PHREEQE—A computer program for geochemical calculations. U.S. Geological Survey Water-Resources Investigations 80–96, 210 p.

Plummer, L.N., D.L. Parkhurst and D.C. Thorstenson, 1983, The development of reaction models for groundwater systems. Geochimica et Cosmochimica Acta 47, 665–686.

Plummer, L.N., D.L. Parkhurst, G.W. Fleming and S.A. Dunkle, 1988, PHRQPITZ—A computer program incorporating Pitzer’s equations for calculation of geochemical reactions in brines. U.S. Geological Survey Water-Resources Investigations Report 88–4153, 310 p.

Reed, M.H., 1982, Calculation of multicomponent chemical equilibria and reaction processes in systems involving minerals, gases and an aqueous phase. Geochimica et Cosmochimica Acta 46, 513–528.


Reed, M. and N. Spycher, 1984, Calculation of pH and mineral equilibria in hydrothermal waters with application to geothermometry and studies of boiling and dilution. Geochimica et Cosmochimica Acta 48, 1479–1492.

Wolery, T.J., 1979, Calculation of chemical equilibrium between aqueous solution and minerals: the EQ3/6 software package. Lawrence Livermore National Laboratory Report UCRL52658, 41 p.

Wolery, T.J., 1983, EQ3NR, a computer program for geochemical aqueous speciation-solubility calculations: user’s guide and documentation. Lawrence Livermore National Laboratory Report UCRL53414, 191 p.

A.2 Geochemical kinetics Lasaga, A.C., 1984, Chemical kinetics of water-rock interactions. Journal of Geophysical

Research 89, 4009–4025. Lasaga, A.C. and R.J. Kirkpatrick (eds.), 1981, Kinetics of Geochemical Processes.

Mineralogical Society of America, Washington, 398 p. Jin, Q. and C.M. Bethke, 2002, Kinetics of electron transfer through the respiratory

chain. Biophysical Journal 83, 1797–1808. Jin, Q. and C.M. Bethke, 2003, A new rate law describing microbial respiration. Applied

and Environmental Microbiology 69, 2340–2348. Jin, Q. and C.M. Bethke, 2005, Predicting the rate of microbial respiration in

geochemical environments. Geochimica et Cosmochimica Acta 69, 1133–1143. Jin, Q. and C.M. Bethke, 2007, The thermodynamics and kinetics of microbial

metabolism. American Journal of Science 307, 643–677.

A.3 Isotopic modeling Bowers, T.S., 1989, Stable isotope signatures of water-rock interaction in midocean

ridge hydrothermal systems: sulfur, oxygen, and hydrogen. Journal of Geophysical Research 94, 5775–5786.

Bowers, T.S. and H.P. Taylor, Jr., 1985, An integrated chemical and stable isotope model of the origin of midocean ridge hot spring systems. Journal of Geophysical Research 90, 12583–12606.

A.4 Compilers and interpreters Aho, A.V., R. Sethi and J.D. Ullman, 1986, Compilers, Principles, Techniques, and Tools.

Addison Wesley, Reading, Massachusetts, 796 p. Donnelly, C. and R. Stallman, 1995, Bison, The YACC-compatible Parser Generator. Free

Software Foundation, Boston, 89 p.

Documents

GWB Reaction Modeling Guide